It is becoming more common for instance, for judges to consider the parents' respective wage earning abilities in making the custody award. The respective attitudes of the parties towards each other, too can be a consideration. Criminal behavior, drug or alcohol abuse are also factors the judge will take into account. If your children are old enough to contribute information about their custody they can't testify, but they can talk to the judge in private. This is to help them avoid the destructive effects of having to say unkind things about either of their parents in front of them.
Judges differ in their opinions about at what age a child's input can be useful.
However, I have had judges who are willing to talk to very young children if the children seem reasonably able to observe their situation, and hence to provide useful information. However, judges are hesitant to take such harsh measures on the first offense. If the illegal behavior continues, the judge is more likely to inflict harsher punishment on the offender. In extreme cases, a judge can even take the lack of cooperation of the custodial parent as a reason to modify the custody order altogether. Your local prosecutor's office is obliged to go after the offending parent for failure to pay child support.