M.E.
Hi K.:
Here is one suggestion for you. Big Brothers/Big Sisters. I have been a big sister for over 8 years in DuPage County. Now that I have started a family of my own and my "little sister" is now a free-wheeling 16 year old, our relationship has moved to a new place where we don't see each other as often. But, my experience in her younger days was great for me, her and her mother (also a single Mom). The time that she and I spent together was fantastic for us to interact like sisters and also gave her Mom that time for herself. We normally saw each other 2-3 times per month.
It is a terrific program and having gone through the screening to participate, I feel that they do a very good job of selecting only the right "bigs" for the program. Not surprisingly, many of the "bigs" that I have interacted with over the years were "littles" when they were kids. They got so much out of the program, that they chose to volunteer their time later in life. I would strongly encourage you to look at this avenue. It is certainly NOT a babysitting service, but it will allow your children to build their own individual relationships with their "big" and have some independence that will hopefully lessen the fighting and disagreeing. It will also give you time either for yourself or to give more one-on-one time to the other children when one or more are with their "bigs".
I believe the starting age is 8, so right now, only your 10 year old would qualify. Here is the website for DuPage county - www.metrofamily.org.
I feel like I am rambling a bit, but feel free to email me if you have any questions.
Good luck!
M.