AITA for not liking my boyfriend's mom?

I (F25) have been with my partner (M31) for a year now. We both come from two different cultures (he is American and I am South Asian). He is an amazing person in every way, and I feel lucky to have him in my life. We met online and have since broke the distance and we're taking steps towards living together. I would love to spend the rest of my life with him but one thing concerns me which is his mother. I do not like her very much and it's causing me some anxiety about the future of our relationship.

To start, I do not feel much of a warmness from her towards me. Since the beginning I have been spoken of with a skeptical tone; she would balance it out by saying a nice comment or two about me but then it would be proceeded with some sort of fear mongering talk about where I am from, how things are in my culture and making assumptions of how that would tie into my character. Before my boyfriend and I met in person for the first time, she told him I must send her my phone number and address details. I didn't mind this as I understood she was concerned for his safety, even though she was treating it like he was not 31 years old. What I did mind was when she followed it up with a joke basically saying "if anything happens to him I will kill you." While I understand jokes are jokes, I had not even met her yet and I was extremely uncomfortable with how comfortable she was saying that to me.

Another thing is that I don't like that she encourages strange and sexual things to my boyfriend. I don't care what she does in her own private life, but she pushed her ways onto him; they had a little house party where she invited a close friend of hers who was her age, in which she asked that friend if she's attracted to my boyfriend because "it's obvious" and went as far as to ask if she'd sleep with him. She then asked my boyfriend if he found her attractive and if he'd sleep with her. My boyfriend told me about this and I was furious. I found it to be extremely inappropriate that she would ask that especially knowing he is in a relationship with me.

The most recent situation was when my boyfriend and I were on the phone together and his mother walked in telling him she and his brother were going out to get food from Five Guys. They asked if he wanted any and he said no, and said "enjoy your Five Guys." She then said jokingly "Ima enjoy Five Guys in my mouth." I didn't care or even think about it because that's the kind of joke she usually makes when I hear her in the background. But the thing is, she would not stop. Not only did she keep saying that, but she started saying "Five Guys in *your* mouth" to him repeatedly despite him being obviously uncomfortable by it. I told my boyfriend that I found the jokes she made to be strange. We had a talk about it, then when I get back from an errand, he tells me that she apparently overheard our conversation and said "What, she can't take a joke?" I feel like not only is it rude and inappropriate to listen in on our conversation but it is also rude to imply I cannot take a joke.

I told my boyfriend how uncomfortable I was and that I feel off, and he told me that it's because we do not know each other. I think that's a fair point, but then he told me that from time to time I should reach out to her and make conversation to build rapport. Up until now it just feels like the responsibility is all on me to make effort and have some sort of relation. Every interaction I've had with her was solely about him and how he's doing. It just makes me extremely unexcited about the process of getting to know her and having a relationship with her.

While I do understand it doesn't seem to matter because it's him I am with, not his mother, I am anxious because I feel like the family I am planning to marry into really matters and if I am already having these kinds of disagreements with his mother then it is only going to get worse if our relationship gets more serious. But on the other hand, maybe I am the problem, maybe I need to lighten up and I'm blowing things out of proportion. AITA for feeling this way about his mom?