Okay just sent the email. Took me a long time to write although it is short. I kept it polite and light, but did ask her to stop sending things out from me and DD as I do do this myself. TBH I think she'll be sweet and apologetic in response, but just concerned she may continue doing it, perhaps not immediately, but she'll look for an excuse and do it now and again. I emphasised it being weird and unnecessary rather than belittling and offensive, and just hope it stops.
In terms of the other issues, the two I am aware of are her buying my parents absolutely huge/expensive Xmas presents. My family are more in for more modest presents. We have the money for big ones, but people don't massively want others buying expensive gifts for them, or to do it themselves. I don't know all the details, but I know the first Xmas she spent with them she went way OTT and they dropped lots of hints and said things but kept it low key. The following year she did the same, and they spoke to her firmly about it. Since then things have calmed down.
The other one is me. When my DD was born and for months afterwards she was constantly buying masses of things. I didn't need or ask for any of them. She bought so many clothes, and most of them have never been worn or hardly at all, a mixture of my not needing them and them really not being my taste. (She's all frilly pink dresses.) She also bought a very big baby rocker that takes up a huge amount of space. I actually had a small one anyway, although my DD just hated rockers, and I don't really know what to do with the one she got, even though I don't want it at all. She is just constantly spending masses of money. There are lots of other examples of her just spending lots and lots. I think it is partly because I am a single mother and she (so long as my brother is included - he's a very high earner) has a lot more money, but we do have enough, and most people would probably see me as fairly privileged. I do find it patronising and a sort of judgment on my lifestyle and choices, but I can support my DD to a very high standard of living, which I am obviously doing.
Ultimately I do think her motives are sort of kind. She is basically trying too hard to fit in with my family, although they have welcomed her very openly, and would defo prefer it if she tried less hard and relaxed a bit.