This is certainly going to feel like being swamped but if the house is in joint names she does have a right to invite family to visit. . However, where does she propose sleeping them if there are already four of you living there?
I think you are going to have to sit down and work out some civilised ground rules for their visit. If she's not prepared to do this and you suggest that she's already being difficult, I suggest you tell her that if she can't behave like an adult you will withdraw from all negotiations regarding the transfer of the mortgage. I don't like the idea of emotional blackmail but until you can go your separate ways, there has to be some discipline in your reationship while you're all living under the same roof.
I suppose, being the school holidays, she has to take her share of looking after her children. Next time you get a partner, avoid one with any children by a previous relationship !
Could you contact her parents and tell them politely that they must understand that rleationships are difficult at the moment but for everybody's sake you expect everyone to behave in a civilised way while they are staying