Not sure how useful this is...the more a person breaks agreements in new poly, the more nervous you get that they will keep breaking them, so the more information/reassurance you ask for, the more agreements you try to make, the more chances (with a person like this...) that you will be disappointed.
I think the therapist wasn't useful, asking you to rebuild trust while you were already IN the process of rebuilding trust. I think your partner needs solo therapy, and in your place, I wouldn't trust them anymore.
And when you are new to poly? No you probably don't want to sleep with somebody who just fucked somebody else an hour ago until you have a week or two to process. That's the whole point of the initial big list of agreements, and asking for and expecting excess care to not hurt your partner, as far as I'm concerned. One you realize your partner isn't a cheater or going to break your trust, that stuff can really fade into the background and become unimportant, but it IS a big deal for a lot of people at the beginning when they are dipping their toes in.
I wouldn't worry about your "hard rules" I'd worry about your partner agreeing to them, then breaking them, then lying about them. Some people will give you flak for having so many "rules" in the first place - but I am like that..start small, and things relax quickly once you feel safe and like you can trust your partner.
I'm often surprised that people on forums (mainly fetlife, but here too) will say that it is YOUR fault for being too ruley when your partner agrees to what you ask, then breaks their agreements, therefore its your problem instead of the "lying/doesn't know how to speak up for themselves" partner. Maybe that's because it's the partner going WTF? that posts, I don't know.
For me, it would be a deal breaker. Half safe sex agreements/half lying to me TWICE. My husband broke our agreements in our first attempt at poly, and it was a deal breaker - we remain good friends but I can't trust my heart to somebody who does that. I cannot trust anybody that lies to my face, and I find it hard to believe that somebody who will lie to my face twice, then make ME do the work of bringing the truth to light, to be anybody that is near ready to be honest and trustworthy.
Happiness will never come to those who fail to appreciate what they already have.