You cannot control other people’s actions, only your reaction.
You’re very upset about their relationship, which is understandable. Try to take a step back from all those emotions and focus on what’s important, your relationship with your mother. You dated this man for 6 months 5 years ago – in the grand scheme of your life, he was just a blip. He is not worth losing your mother, your best friend.
She is an adult and can date who she wants, which I understand is hard to handle. You can feel all the feelings about this, but you don’t have the right to tell her not to date him. It would have been nice if she had come to that conclusion all on her own, but she clearly cares about him and it’s too far gone at this point.
What if you tried accepting this and shifted your focus to rebuilding your relationship? I’m sure she’s only avoiding you because she feels guilty and ashamed and is afraid of your reaction. What if you sent her a message saying you miss her and that you while you know you didn’t react well at first, you love her and want her to be happy. Say you’d like to have a call or meet up and that if she doesn’t want to talk about her new relationship, you don’t have to, but if she does, you promise to be positive and open-minded.
Do you think you can get there? If not, therapy.