Yeah there's a lot going on in this picture.
1) She's only 3. It's a tough age for parents generally, step or otherwise. A new sibling is also a tough new phase for any child. So lot of sympathy towards her.
2) Her "not allowing" you to sit on the couch?? Not ok. It's ok for her to feel possessive, and it's ok to want special time with her Dad. It's not ok to not allow another member of the family to use communal furniture.
Having said that, I think it's important to give 3yr olds control and power where you can. Let them pick their clothes, what bedtime story you read her etc.
3) I'm a bedsharer, so I'm ok with a toddler in my bed. BUT you are not, and it's your family, so you get to decide.
Is she with you guys full-time? If yes, then you guys definitely need to get on the same page and come up with what is ok and what isn't for you both. If she's only there some of the time, then you still need boundaries, but I would make sure she has some serious one on one time with her Dad too.