@soshnomore
I am so sorry you’re deeply hurt. I can only talk from what I have learnt from my experience of seeing my mother losing two husbands..... and moving on twice.
I don’t think your dad has replaced your mum even though it very definitely feels this way to you. It is far more likely that he is using this new woman to give him comfort and lean on her to work through his grief. Ie as an emotional crutch. Some people do this. I know my mother does. He sounds very lost without her and his marriage to your mum seems as if it was very co dependant.
When you are co dependant on the other person, losing them is far harder than if you were more autonomous. As a codependent when your mum died he quite probably felt as though half of him was missing. As he couldn’t stand to feel this way, he quickly looked for comfort, not to replace your mum but so that he didn’t have to feel so utterly lost and afraid.
He may see his finding someone else as him lightening your load and setting you free from feeling responsible for him. So from your dads perspective it may be very difficult to see you unable to be happy for him. Now that he has found this woman, he possibly feels free to lean on this new woman instead of you. He can feel fresh and alive all whilst working through his grief.
I know that’s really really hard thing to understand when it’s not possible for you just to replace your mum.
My mother dated and met someone a couple of years after my dad died. He moved into my family home as soon as I left for to university at 18. She didn’t bother to tell me this was happening. Luckily for me he was a wonderful man and when he died it felt very much like a second parental death.
This time she moved on faster. Six or so months. She does not stop talking about him and when she does, I want to rip her head off. It was a long and very debilitating illness and it was very hard for everyone. When he was dying, she talked about what she would be able to do after he died in front of him. That also really really pissed me off. But I also get that was the only way she could cope with her life and standing by and looking after him as he slowly wasted away.
I have met her new man. He is quite nice and I’m glad I got it over and done with. I didn’t want to do it btw. I am obviously far too old to get involved with him in the way that I did with her second husband. He has kids and grandkids and I don’t want a replacement father or grandfather.
I’m sure she’d like him to visit here in my home. But I’m not ready. I’m glad I met him but overnight stays are not what I want for my family. My dd wants her grandma around, not some bloke in tow.
From your perspective, I really would try to muster the strength to meet this woman. But do it in a public place, not in the house and for a short period. So meeting for a coffee for example. You can escape pretty fast from that one. I’m saying to do it for you so that the heavy weight surrounding her will very probably feel much lighter. You may even like her. And because she knows you are grieving it is ok to be human srojnd her. 
Rosina
It was the same in my family and I was mid teens. My mother never once comforted me when it was her place to do so, me a child and her being the adult. She was horrible to me about him actually, which was bloody hard. She was used to me being her emotional crutch, you see, which I’d been taught to do right from a baby. This time I was far from being able to cope with her feelings, not yet an adult myself. I know the space of time between my mother finding a new man is longer than ops situation. But I found it really hard. She has always made everything all about her.