Child Support Arrangements and Retroactive Collection

I was the custodial parent of my 2 children for 5 1/2 years. During that time my e-wife paid no child support. I our divorce papers she was ordered to pay approx $210.00 a month, I agreed to not start child support at that time because she was going to provide work-related daycare. Sometimes she did provide the care and most times she did not, although my children were old enough to stay home alone. My children are now living with their mother full time, and spending about 30 to 40% of time with me. She has had the kids for approx. 6mo. and now wants child support, even though she never paid. Do I have any right to collect some of the past support she did not pay to offset the anticipated support I must pay. She also chooses not to work, and has gone on to have 3 more children, she is married and her husbands pay covers all of their bills. Thank you for your time and consideration of this issue.