Of course you shouldn't feel obliged to go to this parent's funeral. They were abusive to you so it's entirely understandable that you would feel fake if you did go.
My abusive F died 20 years ago. He had sexually abused DSis and me when we were children (and physically and emotionally too), but we'd repressed the memories of what happened to us, though I'd had strange images for years that I couldn't understand. The things I did remember of the physical and emotional abuse I didn't recognise as such. He'd always been controlling as well, but I didn't recognise that as abuse either. He'd always made my skin crawl and I hated it when he wanted physical contact with me as an adult.
I did grieve for him and I did go to the funeral. My feelings for him were very complex and there was a part of me that still loved him, as I had done as a small child. But at the point where he was dying, I found myself willing him to die, and I felt relief that he was no longer around. I was shocked to discover that there was another part of me that hated him and was glad that he was dead.
I buried those feelings and convinced myself that he was the doting farther that my DM said he was. My DSis was the same.
The scales started to come off my eyes when DH and I started adoption training and we talked about what every child needs and how the most important thing was that a child should feel safe. It was at that point that I realised that I'd never felt safe as a child.
The memories came flooding back when we had young children. It was horrible but also made sense of the conflicted feelings I'd had when my F was alive, and why there had always been a knotted anger inside me.
I also realise now just how bad things were, because I just can't imagine doing any of the things that he did (DM abused us physically as well). I was afraid of him, and I never want my DDs to be afraid of me.
I also feel really sad that I never had the relationship with my parents that I now have with my DDs.
There really is no right or wrong way to feel, that's what I've learnt through this. So you really mustn't think badly of yourself for not wanting to pretend that you had a good relationship with the parent who has died. And don't let anyone guilt trip you into going to the funeral, it's entirely your choice. 