I’m stressed I’m a step parent

I don’t know to begin.. I not very good at this so bare with me.. my husband and I been together for almost 4 years.. we have a 4 month old and his 8 year old.. her mom left her with us last February and moved 6 hours away.. she lived with her and we saw her every other weekend.. and her mom has CF so she is always in the hospital doesn’t take care of herself.. never calls her.. when she finally does call her she tells her she will call in couple days and never does... for half the year she didn’t see or talked to her.. we have an agreement that she spend 4 weeks with her.. she went up and since then I have had problems with her a lot and every time her mom calls she acts out & this year at school she been a bully to her friends and she hasn’t wanted to go to school.. she loves school she always gets up early to go.. past couple weeks she been failing test and homework papers ... she makes herself throw up.. it doesn’t matter what I do nothing works.. she be grounded no friends houses no tv no electronics.. but her dad isn’t home either he works out of town.. but he does call every day twice a day and does come home every three weeks.. her parents has not been together since she was 2.. she has always-lived with her mom.. but her moms bounces between boyfriends and living with her mother..& she has a little boy also.. she writes mommy on papers to me but doesn’t actually say it but my husband calls me my name and not babe hunny or anything.. but everyone baby’s our daughter but im the only one who doesn’t.. I’m a stay home mom who has a very colicky 4 month old then I’m trying to deal with her behavior