If your divorce is final, then the parenting plan you have is a court order. Here is what I would recommend you do:
1. Put it in writing (probably through email) to him that you need him to follow the parenting plan so that you can both live your lives with a dependable schedule. Let him know that you will not allow him to have the kids during your time, and that you expect him to take the kids during his time.
2. Keep a record of every interaction and exchange, noting the dates and times of when he has the kids and when he makes threats.
3. If he does not begin to abide by the parenting plan, contact an attorney. They can help you file a Motion for Contempt, which tells the court that he is not doing what he is supposed to do and that you need them to help change and/or enforce the schedule.
Even if he stops paying child support, that doesn't mean that he doesn't owe it to you. If you think these threats are legitimate, make sure you have some backup financial options in case those payments stop coming for a while. An attorney can also help you file the documents to garnish his wages so that you will receive child support payments directly from his paychecks if he stops paying you himself.
There isn't much you can do about his threats, however if he doesn't follow the court order regarding child support you should go to court to have it enforced. Regarding his not following the visitation schedule, if this is inconvenient you should insist that he follows the schedule. On the other hand, if it's no big deal to accommodate his visitation request it may make things go easier.Good luck.
You've already gotten two good answers to this question. Unfortunately, whether you're divorced or together, there is always the possibility that he will fail to provide financially for the children. Whether it's because he tries to hide from enforcement agencies, or he gets hit by a bus, there are no guarantees when it comes to child support. That can make it extraordinarily difficult to try to plan your financial future.
I would say that one of your biggest issues is the way he's treating you. Men know that they tend to be at a disadvantage in family court, so they often act out, to show you that you're not the boss of them. I think that's why the first answer to your question mentioned e-mailing him about some expectations. It's ok to set reasonable standards, and to expect those standards to be met. For example, if the two of you are meeting for an exchange, you might let him know that on all future exchanges, if he's more than ten minutes late, you're going to leave, if you haven't heard from him. Get it in writing, and make it reasonable.
This advice is based upon limited and hypothetical circumstances. For an answer that is specific to your situation, please consult an attorney. The answering of this question does not create an attorney/client relationship, and the poster should seek additional information from qualified legal counsel. Many attorneys, like ours, offer no-cost consultations.