It's lovely for all the posters saying "can't see the problem", "isn't this what you do for family". That's great for you that you have family who you love and who will respect your home. Good for you.
However you are not the OP and you don't know her mil or her family setup. If she doesn't want them in the house at such short notice then why should she. My husband would never, never do this to me because all family decisions are joint decisions. A compromise may be reached, but not with so little time to work it out.
I'm a mil too and can't imagine ever making a request to stay in my daughters house without a very good reason. It's rude, even for close family.
I would totally freak out at the thought of anyone being in my house while I was on holiday and at such short notice. I would need at least a month to clean everything in sight. It's just the way I am and the OP appears to be the same.
We once let my brother and his girlfriend house sit for us and I would never, never do it again. They were in grotty accommodation and it suited us for some reason that I now forget. We don't smoke, they did, but I asked them not to do it in the house. We came back to an empty house, all windows wide open to clear the house of cigarette smoke and permanent heat marks on our very nice dining table (the only decent piece of furniture we had). My brother is lovely, but I felt like he had no respect for us or our house.
Apart from all of the above, my house is my sanctuary and somewhere to retreat to. For various reasons we have needed this a lot recently. We have overnight visitors all the time, but I would hate them to be there when we are away.
Have a lovely holiday OP.