There are several potential issues or strategies raised by your question. Specific to the title, the only way to get his license reinstated is to have support enforcement lift the suspension. There may be the ability to negotiation with support enforcement with topics such as payment plans or the signing of a waiver that might allow for a lift of the suspension, but there certainly is no gaurantee that they are willing to negotiate.
Ordinarily, I would be telling you more about the possibility of a support modification, but given her threats to withhold visitation, perhaps he might first consider whether his case is ripe for a Parenting Plan modification. One possible basis to modify the Parenting Plan is to reflect what has actually been occurring. If he has a schedule or calendar of the times when he has had Jace in excess of the Parenting Plan, it may be effective evidence in pursuing a Modification.
I agree with Mr. Jones' advice. Some additional evidence which may help in a PP modification is the threat to now strictly enforce the pp if he files an action. Was the threat in writing? Or witnessed by someone other than your son? Your son may be able to obtain legal help through the State Bar Association or other agencies such as NW Legal Foundation. Google WSBA to start getting him help.