Hmmm - I would wonder if your partner actually wants to be in a relationship at all? I spent around 7 years being single and very happy. What I loved most about it was the freedom. I didn't have to make time for a partner's family or engage in activities that I wasn't interested in because it was important to a partner.
I spent my time and energy on the things I wanted to do and on developing relationships with people who shared those interests. The time was lovely and I think the most free I have been in my life.
I also wonder about your partner's perspective that doing things for other people has something to do with monogamy. I have a wonderful and trusted friend. I love her. My relationship with her is very important to me. She's a platonic friend and has always been that way.
Anyway - like I say, that relationship is important to me. So sometimes I do things that I'm not that interested in so that I can spend time with my friend - typically this means spending a Saturday afternoon shopping. My friend's hobby! Not something I find fun at all.
And sometimes I spend time with people I'm not that fussed about. My friend has a friend who can be hard work on nights out so if she is around, then usually I go along to to make up numbers and help balance out the negativity from the difficult person.
And sometimes she does things that she finds difficult for me. We arranged to go walking together once and I was keen to bring one of my dogs along. My friend agreed to that even though she is terrified of dogs - she said she trusted me to make sure it would be fine.
I don't see these things as restrictive, as a sign that my friend owns me, as unhealthy. I just think it's what you do when you are in significant and important relationships - regardless of type of relationship.
I hope you are able to work things out so that you can have a more fulfilled life.