Child support and visitation are not linked. It appears that you may want to take some non legal steps. You may want to go visit him at his home and meet his wife. You may want to have some idea of what the children have at his home. There was nothing above that stands for the proposition that the children should not be at his home overnight.
You can ask the court to not allow out of state travel without your permission and getting specific information about what he plans to do etc. You can ask the court to not allow over night visitation. However, you will have to mention a reason why it should be restrained. Failure to pay child support should not be high on that list.
Hire an attorney -- without one, you will have little chance of success.
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You need a parenting plan to resolve these issues. See my AVVO Legal Guides on child custody, parentage cases, custodial interference and interstate child custody for more information about the legal issues raised by your inquiry. Please keep in mind that although these Legal Guides are often informative, they are no substitute for legal advice from an attorney you have retained for consultation or representation. There are always exceptions to the general rules. Click on my photo. On my AVVO home page click on "Contributor Level - View Contributions" or scroll down further and click on "Contribution - Legal Guides." Scroll down the list of my 29 Legal Guides and select the topics relevant to your question. If you like my answer and Legal Guides, please make sure you mark them as “helpful” or “best answer”.
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When you say he got a Parenting Plan do you mean he had one drawn up by a lawyer but not signed by a judge or commissioner? Has this case been to court yet? Has there been a determination that he is the father of these two boys?
If you have not been to court yet the solution to your problems may be solved by you being more proactive and taking him to court with your own proposed Parenting Plan and the sooner the better. Get a decent lawyer to help you and file right away.