Hello, my name isXXXXX am a licensed attorney and I will be helping you find the answer that you are looking for.
Unfortunately, a contract with the above verbiage (or any other) will not protect you from the power of the court order. In any case that a contract contradicts the court order, the court order will prevail.
This is how it could play out (worst case scenario), your ex signs the agreement, but then as soon as you move in with your boyfriend, he stops paying you alimony. At that point you would have to file a Motion for Enforcement of the Court Order. The court would review the order and would most likely rule in favor of your ex because he is complying with the court order - despite the (effectively meaningless) contract.
Therefore, your best course of action would be to file a Motion to Modify the Divorce Decree. That will allow you to take out the clause about cohabitation and to reduce the child support amount. If you are both in agreement on the issue it should be relatively painless and both of you would be protected from the "what if's."
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