Will this be a full cps investigation?

My fianc� and I have been working on my infidelity & we have had three instances in the past year where she has gotten so angry with me during an argument that she called the cops bc she is dramatic about it & being her feelings are so hurt still that's her response to when she gets so upset. Not to mention she feels comfortable calling the police bc her brother in law is a cop in the next department over from where we live. Our last fight spiraled out of control & she lied saying I pushed her & she had our 1 yr old in her hands. She was so upset & crying bc of something hurtful I said while I was mad too. We do not argue constantly infact these are the only 3 bad fights we've had all year! The cop at the last incident called cps on my fianc� --- my fianc� allowed cps to come to our home & she was told he wasn't an official cps worker but was there to make an assessment. She gave him permission to speack with our child's dr & when he was leaving he told her this was the easiest visit he has ever been on. 4 weeks later he calls her back saying he needs another home visit & he wants us to enroll in this program where we would work with him with a therapist regarding our relationship. Not bc he had a bad resort from my childs dr but bc he looked over the police report & he feels we need it. My fianc� knows this isn't cps so she told him she wasn't interested in his program & he said ok. He called back the next day leaving a threatening message stating him & his supervisor will give me until Tuesday to work with their program & if I don't want to they are going to call cps & file an official report against me. It says this right on the voicemail. I've hired an attorney but he is in court today--- can they do this?? Should my fianc� amend the police report that she LIED on? She was so upset and mad when the cops made her right it. NO charges were filed! And this guy came here and knows there is nothing wrong & our child is not in a violent home! Our dr gave a perfect report! Even stating we have always been a loving caring family! Can they use this scare tactic threatening message to get us to join their program?