YANBU you have been putting yourself last while you are both looking for little DSD and it's been hell, you have had to pretend you haven't had a MC and act normally and now when you have a chance to spend a little bit of time together, he's offered to do this.
I suspect the others are right and it's a combination of paying his mum back/helping her out/dealing with the loss of the baby and everything that's going on with his DD. It's a hugely stressful time for you both.
I don't think you 'owe' his Mum rent or that she needs 'paying back' it's not a jolly, it's a crisis and if she is any kind of a parent/grandparent would not even be thinking in this way (and from your other thread she isn't).
I think you need to talk to DP and tell him how you feel without getting angry about it... tell him what you need from him.
If you are starting the custody case, does it mean you have located her???
Big hugs.
I hope people read your other thread before posting here, but I suspect lots may not, so don't be suprised or hurt if you get a lot of YABU etc - you truely aren't.