Failure to pay child support is considered to be a separate issue from custody, so the fact that he is behind does not entitle you to sole legal and physical custody. Courts decide whether or not to grant custody based on the best interests of the child. There are 13 factors that courts use to make that determination. I put more information about those factors in the links below.
If you think a change of custody is necessary, you should hire an attormey to help you file a motion to modify custody in court. For a free consultation call 612-223-7286.
If you were never married, is there an existing custody or parenting time order in place? If not, then you already have sole legal and physical custody. If there is, then you'd have to go back to court and convince a judge that you should be awarded sole custody - the hardly ever happens unless there is a SERIOUS issue with his parenting - if he isn't putting the children into real danger (i.e., is he hurting the children? using drugs?), then you aren't going to get sole custody if there is already an order in place.