First of all, I don't think you're asking too much. When I hire a sitter, I expect her to be warm and loving with my children, to engage them in fun activities, to keep them safe, and to clean up after herself and the children. It is pretty difficult to try to discuss stuff like this with a current sitter, in terms of changing what they already to-- I've tried this in the past, and the sitter has taken offense. So now what I do is to put all my expectations on the table before they start. And the more specific the better! As for your current sitter, I understand that her mom is a friend, but honestly, I wouldn't use her any more. If her mom asks why you're not hiring her, I'd say something about how you want to use older sitters who can do more with your kids, or something like that.
As for where to find sitters, have you ever tried any sitter sites online? I've had great luck with Care.com. The site is super easy to use and has lots of great articles and tips. They have a huge database of sitters, and you can easily find the ones in your area. They also do background checks (in addition I check references and interview in person). It does cost to join, but I got a discount by using the code CLUBMOM. Well worth the money, imho!
Best of luck to you-- honestly, there are great sitters out there. Don't settle for the bad ones!!!