Anyone with STEP children or have kids with STEP parents?

li
So my SO has a 3 year old daughter that I've been around since she was 11 months old.. 
I often watch her during the week and every time he gets home and is off on the weekend, she acts like a complete brat... 
she's so sweet and such a great listener when it's her and I... also I'm a lot more firm and "strict" as a parent. I don't go for whining for what you want, saying "No!" When told to do something, and I completely believe kids are kids and they should obey their parents/elders. 
Certain things will happen, like if I'm telling her to stop climbing on furniture or to come here for whatever reason.. she sometimes won't listen to me when her dad or HIS parents are around... I'm currently 27weeks pregnant, so I'm beginning to see that I don't agree with a lot  of the things dad and grandparents do as far as (some) parenting choices go... I love her, but she is a complete spoiled brat, doesn't listen, whines for EVERYTHING... but a complete angel when it's just her and myself..
Well her dad doesn't back me up when I tell her to do something and she flat out looks at me in my eye and says "no!"... it's starting to bother me and he gets defensive when I ask him to correct it. Don't know what to do, but when my daughter gets here as becomes of age, this is absolutely NOT the way I want her to conduct herself. As far as getting everything you ask for, not listening to your parents, crying for what you want, etc... if she acts that way towards him, I correct her.. but sometimes he doesn't do that for me.