I get how you feel - I would never charge my sister for babysitting either. If she needed me to help out, I would help out (assuming I was able to). But I guess if it's his relationship, and you can afford it, then no harm?
What’s her financial situation? Maybe this is his way of “taking care of” his sister without being blatant about it because she’s caring for your kids. I would never charge my sister and I know my sisters would never charge me but if the money was needed I can see myself or my sisters graciously accepting the money. Maybe she is in a season.
Honestly I think its wrong on so many different levels. Especially if you've had her children over multiple times and never got offered anything.
We pay my partner's sister (college) when she watches our son overnight, but we don't pay my mom. I think it just depends on the dynamic. I don't see anything "wrong" with paying her, but if you feel strongly about it you could talk to her about it? However, I would be aware that if she were to take offense to the conversation you may very well be out a babysitter for the future, so I guess weigh your options on how much it bothers you.
It's fine. You'd pay someone else to do it and probably a lot more for an overnight. If it makes sense to him, go with it. If she takes the money and doesn't do a good job, that's when it's time to find a new babysitter. Any time you think about saying something though, remember he can't find a new sister...
Since he's paid her, it might be a little awkward not too. But we've paid my husband's brother and his partner to help watch the kids. To be fair, they are struggling to pay rent so this was a way we could help out. I think it really just depends on circumstance and family relationship. Since it's your husband's relationship and he's setting it up, I think it's up to him. Personally, with other parents who have kids, I like reciprocal babysitting. We watch one time and they watch another time.