To obtain a Protective Order there needs to be some threat of physical harm to you, so this would not appear to be an option.
Get the child support and let him file for custody (which usually is a bluff anyway). Your child has a right to that support.
This response does not create an attorney-client relationship and is intended for general information purposes only.
Talk to an attorney in your are a familiar with child custody issues.
The court will make a decision in the best interest of the child. It is unlikely that a court would order you to let him live with you.l
If you have a court order, that is the document that has to be followed, and he can't make conditions on an already approved court order.
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It does not sound like the family abuse threshold for a protective order would be met - simply being annoying and making demands is not enough.
I have to admit that I am a little unclear here - does the child live with you or with the ex? If the child lives with you, you don't have to agree to anything related to letting your ex stay with you in exchange for child support, I would at least set up a consultation with an attorny to get some preliminary advice on your situation. I would not let yourself get bullied into a bad deal for you and your child.