You don't get to include gas in your thoughts on payment for babysitting. It's YOUR choice to WANT to use her, she's doing YOU a favor, not the other way around. Until you figure that out, you're going to be upset over this.
Just because someone is family doesn't mean they get paid any less. That's the most ridiculous thing I've heard. Yes, some family does do it for free, but that's the people who CAN and WANT to do it for free. Your sister wants a fair rate to watch your kids, which you are not paying her. Time to move on.
Diapers realy don't matter either - great that your kids are potty trained...doesn't mean they are any easier to watch. Seriously, pay her fairly and stop thinking you're doing her a favor. Or let her leave and don't make her out to be the bad guy, because she's not.
A fair price for that? I'd do at least $200 a week.
For what it's worth, I pay my sitter $100 a week for my three kids. She comes at 615 and puts them on the bus at 825....so that's $20 per day. The real kicker? She never has to work all 5 days or all 2 (plus a little) hours. Never. But I don't change her pay. Spring break, she won't work at all and she will still get paid. She didn't work a lot of Christmas break-mid-Feb because we had a lot of snow, so a lot of no school days...she got paid for every single one. All holidays, everything. So we are both happy with our arrangement. If she wasn't, I would find someone who was or pay her more...plain and simple. My kids deserve a happy sitter who doesn't HATE coming over...so do yours. And trust me, if she is resenting you for not paying her enough, your kids will know it and that will change their relationship with their aunt. Let it go and move on. Get other childcare.