Need advice/long rant... Sorry in advance!

What the advice is, is for how to be a better step mom. I am a step mom to a 4 almost 5 year old little girl, I've actually known her since she was 3. I've talked to my boyfriend about this only a few times but I honestly can not stand his daughter, I get really annoyed by her and just how he is with her. I've tried and keep trying to connect with her but I just can't.

In the very beginning of our relationship, even before we got together I told him I didn't want to be with him because he has a daughter and with someone I do not like nor do his BM's family like me or my family, yet he convinced me other wise. And within a week of our relationship he wanted me to meet her and I said no because I wasn't ready but he made me stay and play with her. Then after that he just kept pushing her and pushing her to me so I could have some kind of connection but it never happened. And before the relationship could end I got pregnant so I knew I had to build some kind of relationship with her....but it was hard having a rough pregnancy, between sleeping all the time, throwing up every single day/every time I ate, doped up on pain killers because I had horrible stomach problems, having surgery, and being in and out of ER rooms/hospitals...I just couldn't do anything at all...

I've talked to him how I felt, and these are the things that have bothered me. 1) She is very spoiled, like every time we have her she always wants to go to the store buy toys. She will get out of the cart and start throwing anything she wants in the cart and gets mad at him for putting them back. This especially bothered me when we didn't have much money. 2) Every time we did go to the store she always grabs gum...and her mother and I have a mutual feeling about the gum. She doesn't know how to "eat" gum, she'll always have it laying around in chunks and I get worried that my daughter will get to it, and it gets in her hair and her mother gets pissed because she and I have told him time and time again no. 3) When I was cooking for the family she would not eat anything I cooked, even her favorite dishes. And he wouldn't make her eat it, he would automatically give her ice cream. But when we go out to eat it was always pizza and ice cream which bothered me because she needs more verity of fruits and veggies than just junk food. 4) He never says no, just like the few examples already he never says it to her. I understand dads are suppose to spoil there kids but I think its a little too much in his case. 5) He rarely put our daughter on social media but definitely his oldest everywhere...I think its because his BM is on most things but what she's not on is fb and that's where he posts a few more of our baby. 6) When I was pregnant and sick most of the time he would get mad at me because I wasn't bonding with her because I was "in bed all day and not making an effort to get to know her"

There's a lot more but I've been trying to watch her favorite movies with her and take her to a park but he always has something to say or I can't take her because he's not going with us. I even brought her to one of my families get togethers at her favorite pizza place and he got mad because I wasn't suppose to do that without him because he didn't think I wasn't ready for that yet.

Like I said I've talked to him but I know he's not going to change his opinion so I need to take it upon myself to do it.... So any advice?