Not sure how to react

You cannot expect any input with regard to where they live, and 30 minutes is nothing!

Just go with the flow. Your GC is only 3 months old at the minute. You may relish the fact they moved out when he/ she is older, and running all over the house getting into everything! As phoenix says, 30 mins. is nothing.

Early days and can’t be easy for him living in your house however well meaning. Best not to say anything...just be there when needed.

Don’t say anything, if and when they move out your DD will still want to see you, if you upset her by telling her how you feel about the BF she won’t want you around.
Enjoy having the baby with you and try to help them adjust to being a family.

I wouldn't do a thing, because all of those things are between your daughter and her partner.

They are now adults making their own family. I'm afraid how and where they live is totally up to them. Just be friendly and supportive whatever the future brings. Your relationship may improve once you are not actually living on top of each other with the stress of a new baby added in.

There's nothing you can do except wait and see what happens. As others have said 30 mins away is nothing really, it's definitely doable.

Thankyou for your comments

Yes I’d bite your lip, because in the past when I passed comment on my son’s former girlfriends neither thanked me for it and doubled down and stuck up for them. Afterwards they said I was right, but neither wanted to hear it at the time and it probably actually made them stay with the girlfriends for longer as they were being defensive!

Never never discuss your offspring’s partner with them. You will never win and can have the adverse effect.

Wait! Time will tell what you may or may not be needed for!

I also agree with the advice other posters have given you.

Obviously, if you actually know he has abused her, you would wish to say something but I still think you need to be tactful.

Moving 30 minutes away is not far at all. I hope everything works out for you all.

Let them lead their own life ...

Kittymae, I agree with the majority of posters who say bite your lip. It is probably a difficult situation all round and will probably improve once your get your space back and they get theirs. You may find their relationship works much better when they are on their own. You can still be supportive by letting your daughter that you are always there for her and you wish them well. If you make her feel guilty she will resent you.

I would do nothing.
Iwas once told by a doctor who is a relative of mine that often middle aged women come into his surgery with depression and nine times out of ten it is caused by interfering with DD ‘s‘or DS ‘s ideas about their children.
As Notthatoldyet9 says.
Let them get on with it.

Re my previous message.
I don’t have daughters but I was told by the Dr that it is usually the boys mothers who are the worst!

Now that your GC is 3 months old, your DD and BF are very likely ready to cope on their own with the baby. It's lovely for a new mum to have her mum there to begin with, but for the BF it must have been difficult. It's great that the BF is earning more so that they can have their own place. We bring up our children so that they can become autonomous adults. Be glad for them, also glad that they're not moving far away.

Oh gosh they re only moving 30 minutes away don’t be one of these clingy grandmothers They are not an extension of you they are now their own unit to live love and make all their own mistakes

Boys' mothers worst..hmmm. The problem is that boy's mum is still a mum. She believes things have a certain way of being done within a family Dil has a totally different set of ideas. Now, one or other of them starts to object and it's not just about babies, it's all kinds of stuff. I expect it's often mil who thinks she knows best, but not always by any means.

aren't BOTH mothers MIL's.Or are mothers of daughters exempt from being interfering busybodies?

I would be very careful not to be or appear to be critical of DD's boyfriend.

A lot of young people talk to each other in a manner that seems rude, or arrogant to our generation. It is up to your daughter to object if she dislikes it. You should not mention the matter.

The need time to become a family and honestly if they are only moving 30 minutes away, you are very, very fortunate.

My son lives at the other end of the country, and many on GN have children living in other countries.

Well I would leave them to get on with their lives. They have a very young baby. If they move it’s only 30 mins away which is still very close, why are you actually worried they could move close to his family, surely they can live where they chose. Is it because you feel you won’t be able to see your GC as much,

You can't make them live their life how you think it should be. You may well be proved right about the relationship but it is up to your DD to decide on her life. And 30 mins away, oh how I wish I had that instead of 80 mins and 10 hours drive to see GC.

It seems as though you're wasting this precious time by worrying about the future. Enjoy helping with the young baby while you can.

Of course they will want to move out and get their own place. Where it will be is up to them. You can discuss it, express a preference, but not make demands. You may not trust SIL but it's rather more important that your daughter does. He's her choice!