Well thanks for all the replies.
I'm not so sure about the cultural arguments people have come up with. She says she does the same for her own brother and sister, although they also send their own cards to their family too. To me that suggests that it's something she does, and her siblings tolerate it in a way that I won't, rather than being a broader cultural thing. Also, just to be clear, she was born and raised in London, and lives a totally normal independent life for a 29 year old - yes, her family background is Bangladeshi Muslim, but it's not like she is not familiar with more mainstream British culture. I personally think it's far more personality based than anything to do with background - the vast majority of which she openly rejects and eschews, hence the difficulties with her own family. (Her parents have been told she lives with a friend, although my parents and I think think they must know the truth and it's more a "don't ask, don't tell" situation, so everyone can avoid confrontation. She normally visits her parents once a week, although her and my brother do go away, and have just come back from a 2 week holiday. Presumably her parents were told she was on holiday with a friend and just never saw the photos or something. It all sounds weird to me!)
I have not been on holiday with her, and nor would I do that, although she often drops hints about this. I've made a decision to not ever spend the night in the same place as her, because I just find her too much and I've been open with my parents that it's a matter of time before I completely explode. (This is because of her extreme extroversion, combined a bit with the constant control. She just won't shut up at all.) My parents have decided not to have all their children visiting at the same time because there's not enough space and they are getting older and can't handle it. (I have a much younger brother too, with significant disabilities, who mostly lives in residential care, but always comes home whenever anyone else is visiting.) I've not openly asked about it, but imo this is just a pretext for not having her down at the same time as me, which suits me fine, as I wouldn't be doing that anyway! She takes over my DD, leaving everyone else who is related to her feeling like a spare part. Also, she is too OTT for my baby who ends up crying and tired and so on, when other people are more sensitive to the fact that she is overwhelmed, wants a sleep, needs a reassuring Mummy cuddle in a new situation etc, whilst of course adoring her and wanting to play.
SIL is not nasty, or manipulative, but defo controlling and just so loud and imo stupid (I always think this about extreme extroverts - they talk so much, what they say is almost always stupid. She asks you something and you answer but then the next question/issue has no bearing on the first and this goes on and on. I really don't know how my DB can cope with it.) I do also think underlying all this she is absolutely desperate to be accepted and part of the family, but my parents view is very simple: she is my DB chosen life partner (it looks that way), and that is that, and therefore she is part of the family. We'd all prefer it if she relaxed a bit more.
@Firsttimecatlady I hadn't thought about the points you raised (and no need to apologise - there was nothing offensive and they were good points). It wasn't the things to me from my DD that bothered me massively, beyond just not being my cup of tea. I do get that it would be nice for my DD when she is young to have someone helping her with this, and my parents don't live near me and she does, so in some ways there's a fit, and I'd like my DD to be able to do this.
She has agreed to stop, and that's what matters to me. I expect there'll be more issues in the future, not least surrounding my DD, where she just takes over and makes assumptions about what I want, which are often wrong, and I'm left not really knowing what to do. I'm hoping their own children when they come are some time after I'm done, simply so it's more difficult for her to "mother" them together. I've been clear with my parents that I won't be spending either DDs first birthday or Christmas with SIL because I want happy memories and not to be undermined as a mother the whole time by her.