Oh, my gosh--so controlling! I would not stay with anyone for 11 days, esp. with overtired kids b/c of inadequate sleeping arrangements, & no car.
We have stayed with relatives whom we adore, & yet we were all ready to have our own space after just a few days. I can't imagine 11 days. I'm assuming from your original post that this trip is on your DD's and husband's nickel? If the sister is paying for anything, then that does complicate matters, but I'd not go rather than stay for 11 days with the kids getting more overtired & cranky, and the family stepping on each other's toes, by the day.
I agree with the OPs in wondering why DSIL thinks he needs his sister's permission to plan whatever he wants to do?? I don't know what advice to give you for your DD, except to encourage her and DSIL to make whatever decision *they* can agree on w/o regard to the dictates of the sister. I would hope that he would tell his sister, "We're able to stay at X hotel and of course will need a car; we look forward to seeing you." Period. Why should the sister care if they get a rental car? They'd be paying for their own car & hotel. Maybe blame it on the baby & word it as if "we know an overtired little one can spoil the family time for everyone, so we *insist* on getting a hotel so that our time together can be rested and enjoyable."
If you're afraid of butter, use cream. ~~ Julia Child
As you cook, you enjoy omniscience about food that no amount of label reading can match. Having retaken control of the meal from the food scientists, you know exactly what is in it. (Unless you start w/cream of mushroom soup, in which case all bets are off.) To reclaim control over one's food, to take it back from industry & science, is no small thing; indeed, in our time, cooking from scratch qualifies as subversive. ~~ Michael Pollan