To think this is rude

Its possible that they don't realise they are being rude. Some folk lack conversational skills. She obviously enjoys the friendship or wouldnt keep inviting you. I would tell her that you feel awkward when they do that. I wouldnt end the friendship without seeing what her response is.

After reading your post again, I see that it wasn't a one off at all, and that the cousin has been there several times when you have visited and the "in-jokes" have happened on more than one visit. In that case, I think if the friendship is important to you, you arrange to meet up without the cousin being present, even if that means taking your friend to a different venue. You say she never visits you because she can't drive, but could she use public transport /taxi to occasionally come to your house, or as others have suggested, is there somewhere nearer to her that she could get to, where you could meet up? As you describe it, it does seem as if you do all the running, so to speak. If you are happy with that, that's fine, but it seems as if you are becoming unhappy that her cousin is there regularly when you visit, and the in jokes continue - and it is that that needs addressing. Perhaps this friendship has run its course? (Only you can know that, though).
I hope you resolve the issue, but feeling uncomfortable every time you visit can't continue.

It is rude! It reminds me of the 'talking behind hands' we did as children. I found that rude back then, too. So, I never did.

Another more modern day equivalent is when someone discusses something they've seen online or something they wish to buy or, a photo of the other day at the beach etc. and they only show it to a few people around them. It's worse if it's a funny video- because then the person who didn't see it feels more excluded. And as if they're really missing out. Especially if it overtakes the conversation.

It happens to me all too often. I feel that if the person wants to share something on their phone, they are tgen obligated to ensure everyone saw it. But that, too, can seem like an awkward hardship. But it might, at the very least, put an end to the thoughtless practice! ;D

Very rude. I would be questioning whether the friendship is worth saving, this woman seems to be using you.

If you decide this friendship is worth saving Oldwoman why not drop her a line and tell her how you feel?
From your post, it seems this rudeness has happened more than once but was so drawn out this time you were on the point of leaving.
Some people have no idea of social graces and this may be her cousin's ploy, from jealousy, having heard what a good, kind friend you are, always going to her house.
I'm sure they probably saw from your facial expression that this had hurt you.
Your friend may be complicit, or may be bitterly regretting going along with her cousin's manipulation which said, "She's MY relative, she's only YOUR friend."

I hope it all works out for you all.

I agree - it is rude. Maybe stay away and don't be her puppet any longer- find some new friend who values your company and the effort that you go to to be with them -

Extremely rude and unkind, suggest she visits you, because you have always visited her and it might be a change, she must surely be able to find a way of coming to you, or otherwise dont visit as often, now she has a long lost cousin on board.Good Luck

A lot of people are suggesting being blunt and saying how the private jokes make the OP feel. But mostly couple with the ultimatum of "so if you don't stop, I'm leaving/ending our friendship/etc" How about a half-way measure - express how you feel but without the implied ultimatum which immediately has the effect of leaving a nasty smell. Try the explanation, then see over the next couple of visits whether it has made a difference. Then reassess your next step.

Aren't folk complicated!
I think this boils down to whether you feel the friendship is worth saving. If you have lots of shared experiences and it has generally been a two-way thing, you probably need a strategy for trying to stay friends.
I wonder if there was a family fallout of some sort involving her cousin ( maybe even something your friend feels guilty about?) and she is trying to over-compensate by drawing her cousin into the "inner family circle" using a private joke that excludes you? Who knows!
Could you invite her to a cafe not too far away ( even if you need to pick her up). If she asks whether her cousin can come, politely explain you would like time with just the two of you. When you meet up, ask about her cousin and comment on how their relationship must be important to her and they must have a lot of catching up to do. Then you could tactfully say that , just as she and her cousin need time together to cement their relationship, you like time alone with your friend. You could say that their shared private joke which you weren't part of helped you to realise this and actually made you feel awkward a left out.
If you do stay friends, maybe you could later persuade her to try a short bus journey to a cafe somewhere between your homes.
Good luck.

VERY rude. I think I would have accepted it as a one-off, but it's becoming a pattern of behaviour which will continue or even get worse. And that seems to be happening?

If a friend is genuinely afraid of going further than the local shops, I'd be quite happy to accept that. It would be nice if you could get her to go further but a good friend would surely tolerate something which is obviously a big thing for her.
I think it is very rude though, to keep a private joke going which excludes a visitor. I think if it was me, I'd explain that I felt uncomfortable and would prefer it if she didn't do that. If she shrugged off my complaint making me out to be overly sensitive, I'd tell her straight that I was disappointed that she was so dismissive of my feelings and I didn't need friends like that. However, if she was apologetic and agreed not to exclude you again, I'd give her the benefit of the doubt. What I wouldn't do is give up on a long standing friend without trying first.

Yes, very rude and deliberately excluding you. Some very insecure dolescent girls behave in this manner in order to create an exclusive group and bolster their feelings of inadequacy. Now you are a grown woman you do not have to tolerate toxic people. Stay well away. You create your exclusivity.

"However, one of them will say something which causes the other to laugh and then tell me it is "a private joke" but they will then carry on the joke leaving me sitting there with no idea of what they are talking about."

Well, since they used the word 'private' I'd be inclined to respond - 'Well you obviously wish to speak privately and you can't with me here, so I'll leave you to it.' And leave. Any protests I would counter with 'Your private jokes are making me feel excluded so yes, I'd rather leave.'

Don't sit there and simmer. And don't put up with it. You may be right that she's trying to reconnect with her cousin but it's still rude and if you are friends you should feel able to tell her so. If you don't feel you can say this to her, I'd give some thought to how good friends we were.

And whilst I understand some people get a bit hesitant about driving distances, it's still indicative of her attitude. It's too far for her, but not for you. She asks you to do something she wouldn't.

Too far for her to travel, but not too far for you it seems - that's the first decidedly 'non friendly' behaviour. What's wrong with meeting half way, or her making some effort to come to you by cab, unless she is very hard up. As for laughing about private jokes in front of you - and not just once - that is just so rude and outrageous. Do you need this so called friend?

I would have walked out. If your friend asks why, tell her the truth. They are very rude.
I had a friend who would speak in Welsh to another friend in front of me. If I asked what were they saying they would say "Oh nothing important"

I know what that’s like had two friends that were the same. They were close friends too. Often would talk about work
And I didn’t work with them, and comments about others and I always felt uncomfortable, I did distance myself from them in the end. I found they were better separated if I went out with one and not the other. They do say 3 is always difficult.

Very rude and very uncomfortable. I'd have felt the same as you. At least they could have let you in on the joke. I agree with TillyWhiz, two's company, three's a crowd. I've experienced that myself a few times.

Lots of posters homing in on the travel aspect. Sometimes people just lose their bottle and feel frightened to drive. The friendship is not one sided as the friend invites oldwoman70 to her home.
The issue is that the friend was rude and insensitive and not only once.
I agree with previous posters that it’s probably best to say that you’d rather visit when long lost cousin is not there as obviously they have a different history. Best not to dwell on the fact that you felt left out as friend may wrongly interpret this as jealousy.
As others have said, friends come in all shapes and sizes, none are perfect and we must all decide which ones we value warts and all. Good luck old woman, I’m sure you’ll do the best thing for you, you come across as kind and grounded.

I agree with others, it is very bad manners. Why can't they explain the joke to you so that you can enjoy it as well. If it's a one off I'd ignore it, but if it's a regular occurrence when you visit then I think I would say "As you don't wish to share the joke with me I don't want to play gooseberry, so I'll leave you to it" And I would leave.

She's not the nicest if she behaves like this and the fact that you always have to visit her is unfair. The distance is just the same for you. I think I'd quietly let this one slip away. If your phone has ID I'd not answer her calls in future. You deserve nicer friends.

Oldwoman70.What your friend did is the sort of thing observed in school playgrounds where only the 'chosen' are included
This was childish of your friend, and depending on how much you value her friendship, then give her another chance and if it happens again then 'drop' her and find others who have grown up leaving their childhood habits back in the playground.

I think friendship is a two way thing anyway. The fact that you always have to be the one to visit her would make me think that I was the one putting all the effort in. Now you have this situation with her cousin and their "in jokes". Once could have been an oversight, but not each time you visit her.
Time to think if this friendship has run its course. Next time she phones, say " no thank you".

Extremely rude, sounds like you are visiting a nursery school instead of a grown adults home. I don’t like things like this or people who argue in front of people who are visiting, it makes me feel very uncomfortable

The old saying comes to mind ‘ fool me once' shame on me! You take the time to go she doesn’t sound as though she appreciates you going to the trouble.

The fact that she doesn’t make the effort to visit you occasionally would be enough for me to drop this one way ‘friendship’.
Deliberately excluding you from the conversation would be the final nail in the coffin.
Honestly, there are so many lovely people out there so go out and make some new friends who will appreciate you more and forget this horrible woman.