It's pretty obvious why she want's you in her direct site of vision, because if you was alone you'd definitely do stuff she isn't fw. In terms of this, I think its a process of trust or perhaps getting her used to him. Your mom has a right to have these rules and it's because she cares about you, unlike other moms who don't care where or what their daughter is doing. You should try discuss this with your mom/ and with him separately because it's not easy to just gain trust like that straight away.
Alternatively you could be entirely open with your mom and tell her why you actually want to be alone and hear her reaction, and then you could base you decision off that. The reason why I say this is because if she understands your goal then at least she can sympathise and then you both have that agreement, and at least if you are going to do stuff, you do them safely and she isn't going to be worried. If not then it's a discussion you need to have with your mans and to tell him that if he's going to be with you that this is how its going to be "for now", because you don't know, it might get better; tell him this and give him the option to see if he really loves you enough, or if he doesn't then he has the option to leave.
You are very mature to consider this situation but again will you be mentally okay if you break up, are there any other stuff you have that might be ruined if you do it now theoretically