Can you help me be a better DiL?

Not boring at all - I am glad you posted here. We have read so many stories from 'the other side' and it is good to hear a DIL's point of view.
It seems to me that you are doing all you can for the moment and time, patience and goodwill will solve the problem of your MIL's lack of confidence.

Do your MIL and your own mother ever get together? Or do you try to give each of them their own time with your babies? Only you can decide which way would help them both to stop seeing each other as rivals, but as joint helpers in the task of supporting young parents.

Just a couple of simple things to try - on any special occasion for her, write a card from the GC saying how much they love her. Of course, she will know it comes from you, but that is all to the good.
Make a special point of inviting her for tea, or a coffee, or whatever is convenient, and actually tell her how much you have valued her kindness ind appreciate her experience. After all, she brought up the man you love. We are possibly too reticent about making our feelings clear to our loved ones - it is a very British trait.

You sound like a lovely DIL - well done. I can understand MILs and Mothers feeling insecure when their daughter/son suddenly has a "new Mum" and worrying about the relationship. Your MIL you say is already a very insecure lady but surely seeing her DGC once a week and being involved in their and your life will help her to overcome this.
I think you are on the right track and don't need to worry at all about being a "better" DIL . You can continue to reassure her that you are happy to see her and that the babies/children love her to bits.
On the bright side - you will have no shortage of babysitters!

PS how does your own mother feel about this?

You do sound like a sensitive and thoughtful DIL. Why not say to her 'I would love it if you could come more often so the baby doesn't have to spend the first half hour getting to know you again' in your own words, of course.

As a MIL I often feel I am treading on eggshells and when I have visited, I drive away thinking ' oh dear, I hope they didn't take such and such the wrong way.' It's so easy to take offence at the slightest thing, especially when young couples want to do things their own way. If I offer to cook or iron, am I implying they can't cope? If I stay away and wait for an invite, do they think I don't care that they are exhausted? I send a text every morning, asking if any help is needed, how are they all, have they had enough sleep?

In the end, I think the older generation should be just that bit thicker skinned and not take offence or insist on their way being the right way - even if they know they will be proven right later on. We have to be diplomatic and try to fit in - the prize is all those cuddles with our grandchildren.

Offspring My point of view reflects that of Greatnan and gracesmum. You seem to be an ideal daughter-in-law. You are warm-hearted, patient and generous of spirit. It's a fact that some MIL are less confident than others. In order to compensate, they may try too hard, and so appear to be "pushy" KNOW-ALLS. Some MIL need to feel special because they are "needy" due to a less than warm relationship with their own mother. My three daughters-in-law have always treated me with great affection. I agree with GN when she suggests sending a special greetings card, from time to time, containing a personal loving message from the little one. I have a treasure box in which every card from my grandchildren has pride of place. X

Hi Offs[ring I notice you MIL has no daughter of her own so perhaps she just isn't quite used to the mother-daughter too and fro because of this. You can be my DIL anytime you like! I have to say it took a while to shake down into an easy going relationship with my own DIL but after 17 years we get along just fine and she often asks for advice regarding my DS and the DGC so perhaps just time will be the answer for you

Offspring how thoughtful you are as a DIL and how lucky your MIL is to have you,have you thought maybe of letting MIL take your DD for an hour or two out her own and letting them have qualitty time to-gether whilst you relax for a wee while with your new DS, that may give her a more hands one role in the family,and surely she will understand that your little man is clingy to you because you are b/feeding and that is his natural response,I do support nanarosie with your MIL not having a daughter of her own it does make a differance I have seen it with my DSs partners,but I never make a fuss with them.

Thank you all for your responses, I'm so glad I posted here . I am on mumsnet but am looking for those in the same position as MiL and not myself, and I am grateful to have your perspectives.

I have also asked my own Mum what she would like me to do if she was in the same position and she just advised to give MiL time to find her place in the changed family dynamic and make her feel welcome whilst she is doing so.

Thank you for all of the suggestions, I like the idea of DD making something for her that we can attach a special note to. DH speaks to his Dad regularly but I was also thinking that perhaps I could also ring her once a week (outside of our visit) to let her know how the DCs are etc. DD does sometimes have one to one visits with PiL when DH and I have things to do that are no fun for little ones but I can make this more often which might make her feel a little more needed/useful.

FiL also (unintentionally) might make MiL feel more insecure as if he visits without her will comment to her (when MiL makes observations on the DCs) that DD 'always does that' or that DS 'doesn't like to be held that way' which can't make her feel all that good about it either. I might see if DH can intervene on those occasions perhaps to reassure MiL.

I think that the observations of not having daughters of her own are spot on too.

I know that it also needs MiL to relax and realise her important role in our DCs lives but I'd love to assist with this and not allow anything to sour our relationship.