After reading through the posts, the main points I see are:
a) you have no contact (eg, phonecalls-understandable at 5 years old) with your daughter in-between court orders times. She was totally fine and happy with you over Easter, didn't see her in between, then next pick up very riled up and upset. So what is causing this dramatic change in attitude? Obviously we know but need to paint a picture.
b) you need enough time for a pattern to emerge. How many times has this happened?
You need to demonstrate in your application to court at least 3 occasions. I think you have at least 3 so that's good. It's just to show it's not one off situations.
c) Although children do get upset when a grandparent dies, I feel this is being over used as an excuse. The mother is grieving the lose of her mum. She is not protecting your daughter from her own grief. When I was 12 my paternal grandad died. Of course we were all sad but my parents didn't burden me and my sisters with their grief. Obviously they cried but they dealt with the difficult parts together, allowing us kids to grieve without worrying about our parents. I question how much a 5 year old understands about bereavement. I think if they are reassured they can get over it quite quickly.
d) Shutting off dad will cause another bereavement. Your daughter might be thinking "nanny has gone, now daddy might be going too". A confusing thought for a kid to deal with.
e) the ex saying you're not family is her basically say you're not her family. In turn she has lumped your daughter in with that statement. Let her say whatever she likes there. You know the truth. Your daughter is 50% you and the ex can't stand it.
It sounds insane but even though your ex was the one who cheated, she's projecting her lack of self worth and insecurities on you. I've become a bit of an arm chair psychologist, haha. Read so much on this sort of thing and I believe it applies to most situations when people don't act normally. There's nothing new under the sun, as they say. If someone is causing agro and drama it's because they are projecting their problems and fears.
They accuse someone of abuse, lying, cheating etc etc it's because they're abusive, a liar and a cheat.