Firstly, am I understanding this right? P was with S when you met him. Then P started seeing B too? Now P, S and B are in a primary V or triad, or some such?
Where do you fit into all of this? Are you P's secondary? Are you happy with where you are? Are you at all upset that B is moving in whilst you live apart from him? Or is that cool?
You're right - he allowed her to take advantage and have free reign. So often, we place all of the blame on the other woman, other partner, etc. It takes two to tango, for sure.
How has B been with you, aside from these issues? Is she polite to you? Is she friendly?
If she tried to assert her control, that speaks to me of insecurity. Insecurity is more difficult to become angry with than pure malicious behaviour. I don't know the details, but based on what you've said...
I say look at this as a clean slate. Think like a Chess player, not a Checkers player.
In checkers, you only really need to think about your immediate move. So, B has been a bit of a tool (so has P) - you don't feel like helping them. So you don't. Then, what happens down the road? Will things be frosty? Difficult for you?
In chess, you think about the steps ahead of the next step. If you do this one thing, this one time, you're paving the way to a more peaceful future path. Think of yourself. You want an easy life, right? Maybe - just maybe - B won't see you as a threat any more, because you've been willing to help her. If you have her contact details, you could even reach out to her and say "hey, P asked if I could help you move in, since I have a big truck. I'd love to help you out. Would you like that?" This way, your actions won't be misinterpreted - it won't look like you're helping out just to stake your claim or show your connection to P.
I'd word it to P like a 'one last chance' thing, if I were going to go ahead with helping. I'd say that I'm going to wipe the slate clean, but that I won't be a pushover. If there is any more upset, you will withdraw and be involved only with P. That's fair, in my opinion. And on the plus side, you'll be the one who took the upper hand, who proved to take the high ground. That makes you a better longterm partner. If that isn't appreciated in your current partnership, don't worry - someone else will definitely appreciate it.
However, is there more to it than that? This is why I asked whether you are happy with the situation. What else is going on that is making you feel neglected or unhappy?
It is quite plausible that P has a very busy week, if B is moving in. He'll probably have a lot of tidying up to do and loose ends to tie up. If they're working on primary/secondary and B's a primary, you're a secondary, it would stand to reason that she is going to be his priority this week. But, I don't know if that is the case, about your relationship hierarchy (if any)?
me: open poly (31, female)
GF: (41, female) my long-distance, long-term partner
Earth: (35, female) newly dating
Hubby: (38, male) GF's husband
Garcon: (28, male) GF's boyfriend/submissive
“Peace comes from within. Do not seek it without." ~ Buddha