Welcome, mirrorimage. I am also guessing you are outside the U.S. as I have no idea what a "paddy" is. 
Transitions for kids between parents are tough. I believe you that Dad doesn't see these behaviors; he isn't with her long enough. But just imagine how it feels for her to hold herself together in front of him. When she returns to you, she is exhausted and frazzled. You are the "safe" parent. She can be herself with you. Sorry but that means a whole host of ugly that you get to find a way to handle.
My son was extremely difficult at 5. I found reading The Explosive Child helped me to make changes in how I was interacting with him to bring more calm into our house.