talie101, I do feel for you - and for your new man and his daughter. It strikes me that, although some of us might think it sad that this little girl doesn't have any relaxed/fun weekend time with her mum, maybe it's for the best that she doesn't (in a way), because it doesn't sound as though her mum wants this time - and the little girl would, I'm sure, pick up on this resentment if she spent weekend time with her mum. And that would be damaging; a sort of rejection. So as much as caring for his daughter seems to be monopolising your new man's free time, it's possibly in her best interests, given how her mum is.
But the dynamic between your new man and his ex - regardless of whether it's about custody or anything else - is a bit worrying: her being controlling and him doing her bidding for a quiet life will likely impact on you, and in turn your children, down the line, if you stay together. It's early days, and of course you need to see how your relationship evolves, but I'd keep a close eye on this and be prepared to say something at some stage.
It sounds, with him having his DD three nights a week, as if he and his ex are bordering on 50:50 access/custody/whatever you want to call it. If this is the case, would it be workable for them to split this, say, Sunday-Wednesday for one parent, and Thursday-Saturday for the other - or something like this? Then each parent would have some weekend time alone/with a new partner, some weekend time with the daughter, and they would maintain roughly the same division of care? Or would this be unworkable with your new man's work hours? Worth thinking about, maybe.
Rindercella, that's sad - that your DSS's mum didn't want him at the weekend; it's such a different quality of time! I'll be honest and say that I do fear a super stepmum like yourself coming on the scene and eclipsing me - but I hope our circumstances are different enough for that not to happen. Your DSS's mum doesn't sound that interested, so you filled a void - and brilliantly, by the sounds of it. I'm sure it's paid dividends WRT the wellbeing of your DSS. I love my son to bits and do try to enjoy him and make happy memories with him as much as I can, so hopefully any stepmum will be an addition - an enrichment - to our family set-up, rather than a replacement for me, which I think would be sad for both DS and I.
talie101, you could have a valuable role ahead as a stepmum. Good luck with this situation.