Hi
Is your Dad quite tall? Only asking that as rabbits are prey animals so obviously anything very big could make her be a bit scared. Does she let other men pick her up? I've had this with small dogs before with my Dad, one foster, a little 7 month old jack russel, wouldn't let my Dad near her and growled at him when she was on my bed!
Is she an indoor or outdoor bunny? It might be that 'shoving' her downstairs has caused some bad feeling there, mayb when being cleaned out somebody could hold her as they generally don't like loud noises etc.
How old is your bunny? She might have had a bad experience when she was little with men that are similar to your Dad. I'd encourage your Dad not to try picking her up at the mo, as this will make her more wary, and to gradually start offering her treats or something she likes, sit on the floor with her and do it slowly. Let her come up to your Dad, once she realises he is no threat she will be happier. Build up the time and progress onto stroking etc. It is probably fear that is making her bite, it can take a while with these things but worth it in the end. Main thing is not to rush really and do things at rabbits pace.
My girls love my Dad cos whenever they see him coming they know a treat is imminent!!lol Dad's are just no good for bunnies diets!
I hope your Dad and your bunny become better friends soon.
Nicola