Op I really don't think you're unreasonable.
And yes no wonder you're not keen on her.
Her self entitlement clearly shows through.
Set boundaries.
She's monopolising your husband's time and feels she should come above you in the pecking order.
In all my years I don't think I've heard anyone say their husband is going round to look after his sister's kids of a weekend after working a full week, whilst his BIL and sister go on the piss for a jolly.
Her children are at that age where they are a tow, especially the 18 month one, if I were her I would not even be asking the mother to do it for the weekend., let alone asking the brother to drive half an hour there and half hour back to help to put her mind at rest.
Maybe if the brother lived round the corner, but no, at such a distance.
So's shes basically sorted everybodies weekend out for them and probably knows her nice brother will not say no, she clearly is a bit of a queen bee in the family.
She should wait till her children are old enough to get themselves to bed and where it would be easier for grannie to babysit.
Tough, look after your own very small demanding children and don't expect others to give up their weekend for you, if you're that desperate then pay someone to help.
It's about respect.
If this arrangement goes to plan for her, she will do the same again, thinking everthing has run smoothly for her, not knowing her mother hated it and her brother and SIL thought she she was a cheeky cow.
Some people are just too thick skinned and do not respect other people's time at all.
She couldn't do it for you as she is the primary carer of her children and I'm sure her husband the BIL would not be expected to drive over and help if your mother was on her own with your children.
It cannot be reciprocated.