Yanbu OP as Regardless of whether they are well behaved or not, - (and the babysitter seems to indicate they are not )- it's still giving up your one weekday off a week to do childcare and is a huge ask.
Children still require attention. And you can't disappear off for hours doing the errands you want and need to do on a weekday - nor meeting up with your friends. The whole day becomes exhausting and about DCs. And they get hot bothered, bored and tired, which is always risk time for bickering.
If they go to club on the other days, Dsis can just extend club to Fridays as well. It's not for you to fix if her DDs prefer to be at home but won't behave enough for a babysitter.
My Dsis was lovely and helpful but would never have agreed to have my DCs one day a week over summer holidays !
Don't be afraid to answer your Dsis the way mine used to if anyone tried to do a CF ask
"No I can't, I'm busy then. (/I have plans"). Good luck with it".
My Dsis made it really clear that just because she was childfree, it isn't that she doesn't have an already busy life, her sibling's childcare issues are not her problem to fix -"You're their mum, I'm sure you'll sort something out"