I think you and DH need to sit down and re-evaluate things. (And specifically your parenting role).
Completely understand that you're happy to have her there and it's good for you and DH and family bonding. That's a fab attitude to have.
Yes - the situation is unusual. But mum is NR parent, and that happens, and no one bats an eye when it's a dad.
The contact schedule is weird - but I completely disagree with a PP that you should "make a stand" against mum. That's just going to cause all sorts of aggro (and potentially give SD the impression that she's not wanted anywhere). I think your attitude of "this is good for us and we're thrilled to have her more" is ideal.
You should be claiming maintenance. That's the way the system works, and it's not fair to your family or your children not to claim it. That's taking money from the family pockets and stretching finances more than they need to be.
I do understand that putting a claim in might rock the boat and make her revert to 50/50, but that might be good for SD in any case.
You can choose to forgo it, but I don't think it's the right thing to do. And given her attitude so far, she might make noises about 50/50 to slash maintenance - but I think it's unlikely she'll go through with it as it would her cost more in childcare (similar to many NR dads tbh).
Here's the big problem as I see it: "Not sure what to do as starting to parent SD like my own would inevitably cause friction with DH."
This can't (and won't) work. You cannot have a situation where she is in the house full time, the majority of care falls to you, and you aren't allowed the parent her. That's a recipe for chaos and disaster.
You need to chat to DH and start from the drawing board here. The way I see it is you have two options.
EITHER - you do most of the care as at present, but then you act like a parent. You set house rules, you can discipline, you can make decisions about holiday clubs etc etc. You have a full parental role, and can make choices to balance things so you get one on one with the younger kids, and also she gets fun solo activities at other times.
Perhaps she's in holiday club two days a week, they're in nursery a couple. And the last is family day Etc. Whatever works for you. But you're not a fun aunt, you're a full time parent and can make sensible decisions accordingly.
OR
You're a Nacho, fun aunty. But that means childcare is fully down to him. He either fully flexes his work hours and does it himself, or hires a nanny, or books clubs or whatever. You still hang out with her as a fun aunt and you have fun family activities.
But also there will be plenty of times when you aren't there and frankly - even when you are - there needs to be someone with parental responsibilities who can make decisions and discipline etc - which is either him or a childcare professional.
Think about it logically. When they go to school, school is allowed to make decisions, issue punishments etc in loco parentis. You're providing "childcare" but without the ability to manage it in the same way a childcare professional would. It won't work, it's not fair, and you need a reset.