OP, why did you let your DP do this or (of you genuinely didn't realize) how are you dealing with the fact he did this?
I don't mean not invite his mother, I mean blow up your wedding and cause you personally all this stress. Who cares if his mother is upset and whether that relationship can be fixed, you are upset and stressed.
A decent partner would not have done this to you. You may not know his mother well and possible extremely naively thought she would be ok with it, he most definitely knew she'd flip out about it. I'm suspicious he wanted to send a message to her to be honest but that's speculation.
A good partner would have either said 'I would prefer my aunt but it's just a bit of paper to be and my mum will flip out and cause us a load of stress, so let's go with my mum' or 'I realise that I'm not ok pretending to my mum that we're close and that I'm ok with her, but I don't want this to cause a storm around our wedding so I'm going to tell my mum now that I don't want contact with her and not mention anything about this witness thing'.
What he chose was him having the person he wanted there, a very upset mum, a shadow that will always be over your wedding day (for you maybe he doesn't care!) and you being stressed and upset. He got what he wanted at your expense (and his mum's expense but she sounds like a terrible person anyway). He's meant to be in love with you and centering you, but he put himself first.
Have you talked to him about this? Your focus seems to be on fixing the mess he made, but the bigger issue is he decided to make it.