If you lived close to one another, and he moved far away, he would likely be liable for transportation costs. See if you can work it out with him before you take it into court, though.
Let the father worry about trying to get the custody changed. If the only reason your son wants to go live with him is because he gets angry with you, it is highly unlikely that a judge will do a custody reversal for that. Generally a custodial parent must be shown unfit, or there has to be some great benefit to changing custody to the other parent in order for the judge to change custody.
As a step parent myself, I can understand the feeling of wanting to have the support coming in for a change instead of going out, but hopefully everyone can learn to work together for the best interest of the child.
Good Luck!