I can sympathise with this. I used to feel complete horror in public sometimes when she would be a little *%!@ and even had people say to me, 'well mummy should blah blah' staring pointedly at me, horrifying! I wanted a t-shirt that said 'not her mother' with a big arrow.
I didn't have any expectations, and I think that's a good thing, it took YEARS to build love. Most children are REALLY annoying sometimes. Most parents have wanted to strangle their child at some point and that's WITH all the love you have for your own. That's completely normal, it would only be abnormal of course if they reacted to that. Most just leave the room and count to ten and let the other parent step in. So you have that same irritation sometimes but without the love, of course that's hard. Add to that she is being sent in pre loaded with hurtful things to say and do to you both. Right now she's effectively a tiny stranger, an agent of another team sent in with things to say she doesn't understand, with her mum's aim to have you snap and say that's it I don't want to do this.
Under all that bluster that she really doesn't mean and understand, there is a fine little human, and one that can be shaped with consistent fair behaviour, I promise you. Honestly you won't notice it happening at first, but bit by bit you will find the nice little things they do will melt your heart.
I would look for some things which you enjoy to do in common, baking, craft, horse riding, dog walking, anything really. Before you know it you new found mini companion will be brightening up that activity, and trust me no matter what mum says about you, if you spend real time giving the little one real attention, they will happily enjoy your visit and ignore what mum says, it will completely backfire. Now if I hear 'I do this at mums' I say 'well, bad luck, you're not at mums just now so better quit doing it'. As long as dad is consistent and you stick within his style of parenting and let him sort out big discipline it'll be fine.