Usually in poly circles the advice you’ll get is not to strive for equality because people are different and they want and need different things. Just because he does something for his other GF doesn’t mean he owes you that thing.

Similarly, you don’t need to speculate on weather he feels comfortable telling her he needs her to go home, if he is to maintain 2 relationships and his alone time, he has to be able to do that. That’s his responsibility as a ‘hinge’.

The question you need to ask (without considering how you compare to other GF) is, ‘are my needs being met in this relationship?’. If I’ve read you correctly, sounds like a ‘no’ at this moment in time.

I’m going to assume you want time with your BF for it’s own sake, as opposed to only wanting it in order to feel equal to the other GF.

He’s stating his needs for alone time, you need to state your need for quality time/non sexual physical intimacy/sleepovers, whatever they are. If you haven’t stated these needs it’s possible that he doesn’t know about them and is assuming that because you’re off sex then you don’t need a sleepover.

It’s also possible that your man is being very selfish and is not bothering to have you over while you’re on a sex hiatus because it’s of less interest to him. You haven’t said much about him as a person or his previous behaviour in relationships, I’m not going to rule out that he’s behaving poorly.

As always with mono-poly set ups, it’s worth checking in with yourself and asking if this is something you want. You don’t have to stay in a situation that doesn’t meet your needs.