OP, "She's stipulated that unless they have their own room they aren't allowed to stay here.
Is this unreasonable?"
No it's not, it's totally reasonable. They may be cramped at grandparents but they have their own room and presumably the grandparents' thing was always seen as a temporary move this is permanent, presumably.
Agree with TeenAndTween, "The DS with autism moves and has the smallest room and doesn't ever have to share.
When the girls visit, the other boys move around and the girls have a room to themselves."
Remember for your boys this will be four relatively random nights in a month in their own home when three (mostly younger) girls, step sisters, come to stay. But for the girls this is the only four nights a month when they will live with their dad, and stepmum and step siblings who are all boys and mostly all older than them.
If they feel uncomfortable these could end up being four days and nights they dread. If they feel welcomed and accommodated they may love these days and nights.
The fact you are willing to mix your boys in with the girls initially suggest to me you are not really thinking about the girls' needs, especially the fact his eldest is the same age as one of yours. I think it is totally right the mum is looking out for their interests.
OP, can I ask how long you have been together before moving in. I can't see that but I may have missed it.
"Perhaps we are rushing it but the children are happy....that's what we see so we decided to go ahead with it." I think basing it all on how happy 7 children appear is a bit of a mistake. Especially as you haven't yet worked out where everyone is going to sleep, have you already told the kids that they will be coming to stay.