Speaking for myself, I can't think of anything I'd like less than having my DM coming every Saturday and going to my MIL's every Sunday. (They've both been widowed.) I like my space and to chill out with my own family.
But then, I have a complicated relationship with my DM because of the past (she didn't realise it when my F was sexually abusing my DSis and me. She now interferes a lot when we're disciplining our (adopted) DDs of 10 and 7. She jumps in and puts in her contribution, which drives me crazy, not helped by the fact that I'm thinking, 'What makes you think you're an expert on parenting?' I stand up to her now, so it's much easier now.
She does like playing board games with our DDs, though, which gives her a lot of pleasure so I grin and bear it now.
My MIL, on the other hand, lives a 3 hour drive away so we only see her 3 or 4 times a year. She stays with us, which works okay as long as it's for no longer than 3 to 4 days, as she's always tried to have a closer relationship with me than I want.. Or we see her at her house, staying in the local Premier Inn. This doesn't work well, as her house isn't set up for children and I feel like I'm spending my whole time telling the girls off, which makes it very stressful. (I don't have the easiest relationship with her anyway.)
What works best in both cases is if the girls' cousins are there, whether My DSis's DC or my BIL's DC.
I would suggest seeing them on alternate weekends. You could really do with some family time for yourselves.