I'm going to refuse to babysit for distant relatives because they don't allow me to discipline their kids
Why don't they allow you to discipline their children?
Because I'm just a babysitter not a parent.
You should not have to put yourself in a bad position if you have no power to control it. You should talk to the parents about non physical punishment options.
We have already talked about it and it is getting on my nerves, I just want to leave and never do this again.
I think if they can't respect your wishes you should just quit after you are done watching the kids. It is really unfair that they put you in such a bad position and their kids cant behave themselves.