Thanks for your question. Ultimately, you are the one who has to live with your decision, so the decision needs to be yours, but I am hoping I can help you.
As you have seen, alcohol does awful things to our minds - it is actually a mood- strengthener, and by that , I mean that it strengthens the mood that we are in at the time. Drink when you are happy - it will make you more happy. Drink when you are depressed - you will feel more depressed. It sounds like your partner was in a sad place at your family member's funeral, bringing back all sorts of memories from his mums recent funeral. Of course, that is no excuse for his behaviour, but it gives some kind of explanation about why his mood became so desperate.
It sounds as if this incident, the violence, the blackout, the thought of losing you, has brought your partner to his senses regarding drink and I should like to congratulate him for that. It also sounds as if you are both able to support each other through your drinking problems. You are both able to understand where drinking can get you and can both therefore really empathise with each other, and help each other through the bad times. I think this is very positive.
You both also love each other and are happy to be together. Your son likes your new partner. Of course your mum is worried about you, as she probably loves you too and thinks she is doing the best for you by asking you not to see this man, who she has seen being violent in public and going to prison. So I can understand her view point.
But you are 46. You are no longer a child and do not need your mom's permission to see this man, or to be happy. I understand that it would be much better if your mum liked him, but now she will have to be convinced otherwise over time. If I was in your postition, I would explain gently to your mom that you totally understand where she is coming from and what her concerns for her daughter (you) are. (I guess you would also be concerned if it was your son.) Thank her very genuinely for her caring consideration, but let her know that on this occasion, you have given her perspective lots of thought, but would prefer to follow your own instincts, certainly for the time being. Let her know that you are not about to submerse yourself in a violent relationship and (give her your word if you want to) that should your partner be violent to you in the future, you will get out of the situation (you need to do this for yourself, let alone your mom). If you find this difficult to have inconversation, maybe you could post her a letter or write it in a lovely card. tell her that you don't wish to argue with her, or fall out, but that you would love to continue having her friendship and for her to trust your judgement, as the grown up adult that you are.
I think there are very few of us who can say that we haven't done something embarrassing in public, or that we haven't made mistakes and regretted them. Your partner was strong enough to apologise for his behaviour and I believe that says something good about his character. I think you have something that it would be difficult to throw away and you might then spend the rest of your life regretting and blaiming your mom for. If it comes to an end by your decision, then so be it, but we cannot live our life for someone else, no matter how much they love us.
I sincerely XXXXX XXXXX mom is able to support you in your decision, if only because you are her daughter and that she loves you.
Best Wishes, Sarah