Recently some things have been playing on my mind about my relationship with my partner. After my mum overheard me talking to him on the phone the other day and was shocked and worried about what she heard, I've decided to reach out and get some advice/the opinion of a neutral third party. What she overheard was me trying to comfort my partner about the following. I am on holiday with my family and without my partner and I am meant to be returning at the end of the week. We were chatting about when l'm coming back and he asked if I could stay longer here. I said easily, it's beautiful and I'm really enjoying my time here. He then became upset and said that I must not miss him as much as he misses me, because if I missed him, I would want to return home at the end of the week. I tried to
reassure him that I did miss him, I was just having a really nice time in a beautiful place. He didn't seem convinced. My mum said I shouldn't have to reassure someone in this way, and that his method of questioning me was manipulative and controlling.
I see where she's coming from, but he has a heart of gold and I know it just comes from a place of insecurity.
Some other things that have been concerning me:

-l want to go and visit my friend in a foreign country. She lives with male flat mates. He said he would not be comfortable with me staying at her flat because of the male flatmates, and that it was not appropriate for me to stay there because I am in a relationship. Again, if I were to stay there it would be a dealbreaker for him. He suggested he come to the city where my friend lives with me, we stay in a hotel together and I visit my friend during the day.
-He does not think it is appropriate for me ever to accept a drink in a bar or club because there is a possibility that the man offering would be attractive by his standards, and he would be hurt, even if I had no attraction towards this man. He believes that you should avoid all situations that could cause potential hurt to your partner
-he says he doesn't want a bisexual partner and that he finds bisexuality 'greedy’ I have
experimented with girls in the past but had no sexual/romantic attraction towards them, he became upset when he found out but moved past it as long as I reassured him that there was no attraction involved
-he does not think it is appropriate to travel alone in a relationship. We did agree that ifl could go clubbing he could travel alone because these are our respective hobbies but in retrospect this arrangement seems unfair

l am worried because my mum says a partner should trust you to not break any boundaries no matter where you are, who your with and what your doing. If they don't trust you, there is no relationship.

I don't know what to think. I love this man but my mums reaction has unsettled me and l am looking for an outsiders point of view on the situation.