Basically YOU pay what SHE asks or you find someone else. It is not up to YOU to set the price, it is up to YOU to find someone you trust and someone the kids like. That is the most important high priority. After that if you can’t afford the price you should truly consider going out less often, rather than complain about how much your babysitter charges.
It is a foolish concept to hire a sitter “every” Motzei Shabbos to go out with your friends whether it is to dinner, or to dinner and a movie or whatever and yet constantly complain how much the sitter cost. I find it utterly amusing how people try to cut corners and be “financially responsible” when it comes time to pay someone else, yet they can spend whatever they choose on the night out.
If you only go out once in a while the cost of a good reliable babysitter won’t break your budget. If you go out all the time, then you can afford to pay the price as well.
Ask yourselves this “how much is peace of mind worth to you?” But of course, this is only MHO.