Well I had a response last night. She was sweet and polite and has agreed to stop. She said that she does do these things for her family, although of course people also send their own cards - apparently it's a sign of "unity". Also, apparently my mother told her she liked receiving "whole family" cards. I'm sure my DM did say that, although less sure if it's true, particularly as they are not really whole family cards - I mean I didn't even know about them! Also, although I do find it weird and controlling, it is at least a general thing rather than specifically because of my situation as a lone parent, which was a big part of what had been bugging me.
I actually was less bothered by the cards sent to me "from" my daughter. They were twee and not to my taste but I could just chuck them. My email did not mention these at all, only the cards to others purportedly being "from" me and DD, which did annoy me, but she has asked about this too, and I think I'll ask her to stop. If nothing else to say otherwise feels bad when they are quite expensive and she apparently has plans to do so on my bday and Christmas as well as mothers day! I do accept this was a very kind and thoughtful thing - just not my cup of tea - and it was really the things from me to others that I was getting irritated by.
To those that commented on the use of email...there's a mixture of reasons. I don't use What's App and have never texted or phoned her. I don't really want to develop that kind of relationship, not least because I imagine it might be quite intense. She's not a bad person, just someone I have nothing at all in common with, and whilst I don't want to start a family war, I also don't want to spend masses of time with her. That would mean only raising it when I met with her, and I'm just not sure I'd be able to. Via email I could keep it sweet and light. I just wouldn't be able to do it "light" in person; I think my strength of feeling and offence would come through and she'd get upset and you can never be sure what might be said in the end. With email I can take my time and think and for me it's better in all the circumstances, although in an ideal world this would be something maybe you could talk about.
Anyway, was relieved by the general consensus that people would find this annoying, and enjoyed some of the suggestions - particularly sending her family rubbish presents and saying they were from her! - but ultimately I just want it to stop with no bad feelings running forward, and it looks like that has been achieved.