I can see both sides, you are very lucky to have family so willing to help, many don't, so thats a real blessing for you & your DCs
BUT, I have a MIL, who very occasionally will baby sit, but has to stay over, &as much as I love her to bits, she just doesn't respect personal space in the way my own family do, for example, she thinks nothing of letting herself into our bedroom at the first sound she hears,,,shes an early riser, so can even be 6 am & plonks herself on the bottom of our bed & starts chatting, or walking into the bathroom & sitting on the edge of the bath for a chat whilst I'm getting washed......it drives me NUTS, along with a lot of other silly little things she does, like wet spoons in the sugar, lighting up a cigaratte to smoke outside, in the house & then walking through the house with it , shouting at anything we put on TV because SHE hates TV etc etc, so much so that I'd rather not bother with her babysitting at all,
DH sees no wrong in this, as its what he's grown up with, & he thinks its sweet, & its because she sees me as a DD too, but to me its just infuriating...yet I do see that its because she likes me & feels comfortable with me........but i was just brought up differently & personal space was something to be respected.
So I wonder, as your DH has spoken up about them both staying, is really to do with your Dad not respecting DHs personal space & needing to chill & not have to put on a polite face & chat to your Dad after a day at work etc...........IF you can get your Dad to understand this & a TV in their own bedroom etc, then perhaps you can work it out??
Sadly my MIL, just didn't register DH telling her to stay out of our bedroom etc, well lasted about twice, so we've pretty much given up, which sadly I know upsets her, but she is very stuck in her ways, & won't budge
good luck