I may have missed something critical but did your partner tell you his mom consider you as lesser in some way? Or did you infer that? Maybe his mom is uncomfortable with having your mom over for the holidays for totally different reasons.
If you want to feel confident as having importance in his life, then act like it. Partners talk directly to parents sometimes. In this case, it would have been better to ask his mom directly if it was ok to add your mom to the holiday mix. Perhaps you could think about apologizing to his mom for putting her in an awkward position. Yes, she should have told you of the discomfort long before this. And P should have just refused to be an intermediary if he was that unhappy about it. But apologizing may allow you to act as a person who counts in his life - which you are to all appearances - and it might clear the air with his mom, who just might tell you why she does not want your mom to join them this year.
I think you are struggling with a lot of issues many mono/poly folks struggle with. I see that you are doing the best you can and your willingness to keep trying and working on yourself is really commendable. I've enjoyed reading your blog.