wa alaykum us-Salaam
if i were in your shoes i would keep talking and talking (i.e keep in contact with her). keep upholding ties no matter what she insisted.
never break it off, no matter how many times she insisted she never wanted to talk to you again. just keep on persisting. there is a saying that goes "kindness kills." and what that means is that the more you are kind to someone, the more their heart softens towards you, even if they may dislike you strongly. so if you want you mum to speak to you and if you want to have a good relationship with her keep being kind to her even is she doesn't respond or even if she seems like she doesn't care. deep down she does, she just may not show it. so yes, just keep being nie to her, buy her things she like, do favors for her, and just generally do whatever you feel she likes (as long as it doesn't consist of disobedience to Allah).
even if she reciprocates it with annoyance, etc dont let it bother you. how she acts towards you and how you react are 2 different things.
having said that, be considerate and kind towards her with wisdom. so, for example, don't ring her when you know she is tired. or try be nice when she in angry. weigh everything and the possible consequence (good or bad) up and see what is the best thing to do and when.
may allah soften your mothers heart towards you.