Welcome to our forum.
It is not hard to understand that you miss P, and want to consider his offer to give it another try. I think it is fair for him to accept your relationship with T, especially if he has a new relationship of his own.
Besides that, I think P should have some kind of plan in mind for how things can be better this time around. I would recommend asking him about that and having him think about it and come up with something (if he hasn't already).
I am glad you and T have formed such a wonderful connection. I definitely think you should keep that, regardless of what happens with negotiations with P.
Hope this helps,
Love means never having to say, "Put down that meat cleaver!"