From what you've described, it sounds like your daughter has learned that her dad is the disciplinarian, and when he's not around, she can get away with bad behavior. A good question to ask yourself is, "Are we consistent when disciplining our daughter?" If her father is more strict, and doesn't let her "get away" with certain things, while you are more lenient, she has learned that she can act differently depending upon which parent she's with.
Have a discussion with her dad about discipline. Be sure that you agree on how you handle discipline issues. Kids behave best when they have consistent rules and guidelines, so write a list a rules for your daughter to follow and post them on the refrigerator so that she knows the rules are the same no matter who is caring for her. Of course, you and her father need to be in agreement on these rules. If she breaks a rule, be sure that you and her father are issuing the same consequence for her. Follow through is very important when disciplining.
If you find that consistent discipline isn't helping your daughter behave better when her father leaves, she may be acting out as a way of gaining attention from him. Does she spend adequate time with her dad? Does she feel like she has his undivided attention when they do spend time together? Kids act out when they can't appropriately verbalize what they are feeling. Think about other things that could be fueling your daughter's behavior and talk with her about it.
Yes, a possible reason for your daughter acting up around you is because she feels comfortable in your company. Kids do not usually act up in front of people that they are intimidated by. Take it as a positive sign if your child acts up in front of you.