Thank you so much for replies! I am catching up slowly - apologies if I miss anything.
@EllieQ, yes, that's right! It's not exactly a class thing; it's that my partner feels as if I'm judging her upbringing when I disagree with her, and tends to see my preferences as just snobbery (eg., about eating at the table rather than on the sofa).
@RueRue, that's hugely helpful to hear. I have been trying to include DD - both before DP and I decided on the split, and during the process - because I'd read it was good for her to know she is being listened to and taken account of. I hadn't thought of her self-regulating, the way you describe. At the moment, she won't, but it's rough for her and I am trying to minimise the extent to which she has to make any decisions, because they can make her feel she is choosing between me and DP. I am reassured by the idea that, when we are in different houses, DD might actually find it helpful to contribute to some of the plans about reducing screen time etc.
@Consideratestone, we'll be 50/50. The way I see it is that, at the moment, there is no structure at all, and I feel really uncomfortable with various things. Yes, splitting up means DD will have two sets of 'house rules'. But I can provide her with stability at my house, 50% of the time. That's surely better than no structure at all. And I really have exhausted the options in terms of negotiating with DP. I had a less-than-ideal childhood with two parents who perhaps should have split up, and I'm not at all convinced that two homes are automatically more disruptive than one. I think DD needs at least one parent who is giving her a sense of stability. Don't get me wrong - DP has many good points and I think she truly believes she's being a good parent. But I also think she's confusing doing things that make DD happy in the short term (like letting her stay up watching videos or feeding her cake for breakfast) with things that are actually going to benefit her long term.
@redjoker - I am getting the jist, but honestly, it is so helpful to read. I really appreciate it all. Likewise, @Curlewwoohoo, the detail is really useful!
@Mariposista, thanks, that's very kind of you.
@Isthiswinter - YY, the getting dressed is an issue. When DD was at nursery, I occasionally had to help her button or zip something, but basically, when she was 3/4 she was able to get herself dressed, sometimes quite slowly. Then DP decided that it was absolutely crucial for her to get dressed asap. And it'd be 'hurry up! Quick! Now you're making us late! I'm so cross! Hurry up!' I found it incredibly stressful and one of the things that cemented problems, for me, was trying to explain to DP that it wasn't necessary to make your 4/5 year old cry every morning, when she wasn't even that late. I ended up helping her get dressed to avoid all of that. But I think, probably, once that stress is removed, she'll just get dressed herself. And I will have to just cross my fingers about what happens in her other house.
If you want more structure, less screen time but extra curriculars aren't right for your DD at the moment, you could set aside time for regular activities eg a board game night, play dates, walks, craft/baking/cooking night etc. At that age, one of my DC's friends used to cook dinner with his sister once a week (under supervision). @GingembreThe, that's a lovely idea.
@Monkeyfloor - well, she has her plus points. I suppose what I mean is, she honestly thinks she's being a good mum, and I'm sure she'd find many things to criticise about me.
@Singleandfab - yes, we've already talked (DD and I) about how there will be different routines in each house. And thank you!
@Goinggreymammy - that's a really nice idea, about choosing specific programmes.
Sorry for writing such a mammoth response post, but thanks again, everyone!