There are two types of divorces

contested and uncontested. If you cannot part way with your hu*****and on a friendly term, you will have to go the court for a contested divorce. Note that fewer lawyers are willing to help you on a contested divorce as it can get very emotional and requires more than basic lawyering skills. In addition, I don't think attorneys are allowed to charge you on a contingent basis by ABA's ethical rules.

What you may want to consider it to get divorced first and sue for child support later, if you do get the children's custody. You definitely need to talk to a lawyer now.