C.M.
My stepdaughter is often rude and misbehaves after visits with her mom. She's always been that way. Her mom's house is chaos with crying babies and no routine. There's lots of yelling and she is ignored. So when she comes to our house she's still stressed from her weekend at Mom's.
I doubt is has anything to do with your fiancé. OR, if it does, it's because he's the father "figure" at your house.
What works for us is a buffer between houses. Instead of going straight home to a routine, we go to the park, or dad takes her out to lunch. During the buffer time we overlook rudeness (as best we can) and we try to focus on positive things. Running around the park or eating out allow her to de-stress and transition more easily. If it's not possible to go anywhere, we just let her go into her room and play by herself for a while. We leave her alone. She always comes out a more C. person, more like herself.
It sounds like her dad is a mean person, so she's picking up the meaness at his house. Kids pick up on that kind of thing, and they are little mirrors. They will mirror back the behavior they see. So she comes back to your house a "mean" person.
It's hard for any child to go between homes and yours is only 3. A buffer time and also overlooking the behavior at first will help. Give your child time to re-adjust to your house before you start in with rules. Sometimes it takes as long as a day to re-adjust. Be patient. We've been dealing with this for a long time, and at age 10 she still needs a buffer. So it works with kids of any age.
Good luck!