I am sorry you are dealing with this. I am going to tell you about my parents in the hope that it gives you some perspective.
My parents divorced 25 years ago when I was 5. My dad had an affair with his secretary who he is now married to (has been for 22 years). For the first few years my mum had a few different boyfriends but in the last 20 years hasn't dated anyone. She is not over my dad, but also she hates him.
My relationship with my Dad was confusing when we were growing up. They arranged that he could have us every other weekend for the whole weekend but in reality he would come and take us out on a Saturday once every three weeks. He moved for work a lot so lived a fair distance from us. His new wife had two kids herself from a past marriage and she left them with her ex too so it was just the two of them.
(I never understood this but I can see now that they couldn't have me and my siblings my mum wouldn't allow it - so they couldn't have her kids either as it wouldn't be fair to us or Dad - so I get it now).
My Dad often asked about mum but never talked badly about her, ever. My mum on the other hand talked all sorts of shit about my dad and would always complain that he didn't do enough for us kids, wasn't a good dad and didn't love us.
For years I was on her side, because that was the side that I heard and because when someone cheats you always take the hurt party's side right?
But that was when I was younger, in the last 5 years or so my thoughts on it all have evolved.
First off I had kids of my own and I realised that no matter what happened between my husband and me I would NEVER let my kids think that their Dad didn't love them. I wouldn't talk crap about him and try to discredit what relationship they did have. My kids come first and while I can understand that my mum is hurt by my Dad's actions what I can't understand is why she let it hurt us too.
Secondly, my Dad and the woman he left my mum for are still happily married. I am not her biggest fan but my Dad is obviously happy with her, he didn't leave my mum for nothing. He handled the situation wrong and the ends don't justify the means but I can see that affair or not my parents marriage wasn't working and wasn't going to last. You said that your mum told your dad she never loved him and he insisted on going forward anyway. Sounds like your parents marriage wasn't the strongest either.
Thirdly, I can see that my mum isn't a nice person to be around all of the time. Don't get me wrong I do love her but she is judgmental and picky and she has these periods of depression when she drags everyone down with her. She is also super stubborn and she has never forgiven my dad for what he did, that's not because what he did was so terrible but because of her personality.
I lost the relationships with my dads side of the family because my mum wouldn't talk to them either and now my family has a massive split of mums side and dads side who have nothing to do with one another and it is very awkward. My dad is one of three and his two sisters are both divorced and re-married. When my Dad's mum passed away 5 years ago my aunt's ex-husbands both came to the funeral and my mum didn't which was weird, I almost felt like apologizing for her absence.
And my mums side of the family detest my dad and he is not to be mentioned around them - but he is my dad so that's awkward too. When I graduated both my parents came, my step-mum didn't. It was awkward, we went for a meal and my parents kind of talked around each other and my Aunt (mum's sister) made a few rude comments. My Granddad refused to come, because of my dad being there and that really upset me, he said he would do weddings but couldn't do this - sadly my Granddad died before I was married and I never quite forgave him for missing my graduation. My graduation was about me - your wedding is about you - really the adults should be able to see that and put you first on such an important day.
(I want to mention here that when my dad left he didn't tell my mum why or where he was going and my Granddad was the one who drove her all over the country looking for him, he was also the one who looked after us when my mum worked and was like a father to us so it was hard that he did that.)
Anyway at my sisters wedding everyone was there - it was the first time my mum and dad and step-mum were all together. Mum started to complain to my sister but I stopped her and told her to complain to me and not ruin my sisters big day. Dad and step mum kept to themselves but at one point my step-mum went up and introduced herself to my mum - my mum responded by say 'oh I know who you are' and walking off.
It made me realize that my step-mum had been thinking about it, was probably nervous but decided to do the right thing and try to be friendly. It also made me realize that my mum was acting childish. After 22 years at her daughters wedding she couldn't drop it and give a polite smile and move on.
Anyway my long winded point is, sometimes marriages fail and it is easy to take sides but its not always black and white and the way people act AFTER the marriage fails - particularly where the kids are concerned - is just as important as how they acted in the marriage.
You are well within your rights to be angry with you dad and you don't have to betray him or even forgive your mum to be able to have a relationship with her.
If you ever need to talk feel free to PM me.
Good luck with the wedding