Don't go. It's started off like this and won't get better. She's taking the piss from the get-go!
There'll be resentment about who gets the better bedrooms as there is unlikely to be three equally as good all with ensuites.
Hiring one car will be crap. They'll take it to go off all day and you'll be stuck where you are in the middle of nowhere - or you can go with them and suffer from the lack of autonomy.
The food and drink situation at the villa and out for meals will be a minefield. The mother will take over the shopping buying stuff that her family, especially the teens like, that'll you'll be contributing to that either 1) you wouldn't choose and won't eat or 2) when you do want to go and get one of the pack of 8 icecreams bought so everyone has one, your one has been eaten by someone else, probably one of the kids.
Even if you just put in the amount you eat plus tip on the table when the bill comes in a restaurant the mother will put it all on her card, and either only put a nominal tip in or no tip, so your tip will subsidise them.
It's very hard to get it equal but she's made no attempt to from the start so take that as your warning. I'd be bending over backwards to make it fair and would make that clear to everyone to reassure them. For example, saying we'll pay two-thirds accommodation also 2/3 basic food kitty with any extras only the kids eat kept separate. She's taking the piss already and if you pull her up on it there'll be the eye roll and "how petty of you, of course we'll keep it to the penny if you're that bothered" with all the passive aggressive "no, no, no, we'll put an extra EUR 1.7 in as we don't want anyone getting upset, do we".
Then there'll be the teen crap, arguing with parents, mess. The hell of living in close proximity with people and their habits, especially if you don't get the nicest room with the ensuite - there'll be sharing of bathrooms with teenagers, skid marks in loo, wet towels everywhere, hairs left in the shower, teen DD using your nice toiletries etc.
I've done it. We're not friends now. Never again. Any irritations will be magnified to the nth degree. You'll hate everything about them when you get back and while there will be constantly on your guard waiting for the next piss take.