Unfortunately, you would have to include your request to incorporate your separation agreement into your divorce complaint. Since you are already divorced, the hearing has already been held and it is too late now to incorporate it. Most SAs are never incorporated however, and your SA is still enforceable as-is.
Alimony in an agreement is not modifiable unless the payee agrees to a new amount. If not specifically stated in the agreement or order that alimony terminates on cohabitation/remarriage then it may not. Since your alimony is set forth in a separation agreement it is non-modifiable but does terminate upon the remarriage or cohabitation of the payee spouse if those terminating factors are listed in the agreement. If the dependent spouse is living with someone with whom they are engaged in a romantic relationship the supporting spouse may stop paying alimony according to the Agreement.
If the dependent spouse then attempts to sue for breach of contract the supporting spouse will need to prove the cohabitation. Using a PI to gather evidence of the comings and goings of the paramour will be helpful, and if a lawsuit is filed you may subpoena financial records and other documents (bills, bank statements, ect) to prove the cohabitation.
Finally, if cohabitation is not listed in the agreement as a terminating factor, the court will NOT insert it as one. Cohabitation is grounds to terminate alimony, unless the agreement does not provide for cohabitation to terminate payments.