You may petition to terminate visitation rights under the circumstances, requiring him to litigate re-establishing them if he ever comes back. You should petition for the arrears, asking for service to be determined by the court in lieu of the other methods upon a showing of a failure of locating him after a duly diligent search (e.g. private eye does one or more searches, etc.). The substituted service provides jurisdiction and then the matter takes place ex parte or by default.
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There are definitely legal steps that you can take to protect yourself and your child under the circumstances. It sounds as though your concerns are warranted, and I recommend that you speak with an attorney as soon as possible. You should not wait for the father to return to take action, as it may already be too late at that time.
The above is not legal advice. You should consult with an attorney immediately.
Your case raises a crisis of credibility.
You cannot get a family court judge to sit with you in your living room and watch the man's behaviors. So if you go to court, either you will be believed or he will be believed. So many Referees, Commissioners and other under-judges believe they are lie detectors. They take a look at a litigant's infra-red rays and make snap decisions about their truthfulness. Many times these days, having a well connected lawyer helps.
The court may or may not believe that you had the man served properly for him to appear. If you serve him properly, he can appear and say that you are lying and the you withheld visits. The court may or may not believe him.
As to child support, the picture is different. He must pay according to the order or else you can file a violation petition against him. Will he be able to pay all he owes is certainly another story and all the jailing in the world may be unable to loosen up some money for your child. He'll play on your heart strings to waive arrears or drop the support amount and you may or may not.
Another option which no lawyer would recommend is to do nothing. Enjoy your children and the peace of having no government in your life. You have a twenty year statute of limitations on support and you could decide to go after him later assuming that matters to him.