I had to deal with a similar situation when my son was almost 2 - my husband was in the Army and sent to South Korea for 15 months. He left when my son was 7 months old and returned right before his 2nd birthday. It was hard for my husband to deal with the fact that to our son, he was essentially a stranger. He would scream and cry if I wasn't the one who fixed his breakfast, got him dressed, put him in the car, not to even mention what it was like if I tried to leave the house and leave him home with Daddy!! It became clear that the only way to extinguish this behavior was for me to completely step out of the situation. He needed to learn that regardless of his preference, Daddy was home and had just as much a "right" or "say" in parenting as I did. The more I stayed in the situation trying to "reassure" or "soothe" the more extreme and dramatic his reaction to Daddy was. Within a short period of time, he learned that Daddy was no different than Mommy when it came to following his directions, listening to what he said, and having Daddy do daily parenting tasks. Within 6 months it was like Daddy had never been gone. I am convinced, though, that it would have been a shorter time if I had stepped back sooner. We spent weeks trying to "explain" and rationalize with him, and me trying to remain a comforting presence in the new situation. All we accomplished was making each situation MORE dramatic and MORE traumatic. Once I decided to step back, our son realized that the only choice in the situation was to deal with Daddy. This realization immediately reduced the drama and the relationship improved dramatically.
Good luck! I say you need to step back. Let dad take control of those situations without you stepping in and interfering or offering ANY alternative. Once your daughter realizes that there is NO other option other than dealing with Daddy, I really believe the drama will go away. At this age, I don't think she is really capable of being too concerned about hurting Daddy's feelings. All she knows is that if she pitches a big enough fit, eventually the person she wants to do everything will step in and do it. If this behavior stops working and Mommy doesn't step in and do it instead of Daddy, the behavior will stop too. Explain to her ahead of time that tonight Daddy is going to do this, this and this. Period. No matter how many times she gets up looking for you to "redo" it, you are NOT available and Daddy is the only one to put her back to bed. It will probably hurt your husband's feelings a lot less if he feels he isn't going to be over-ruled by a 3 year old. Every time you re-tuck her in, it is like telling her that her treatment of her Daddy is valid and acceptable, which it isn't. The same thing holds with you and the jacket. If it doesn't bother you, fine. But every time you let her dictact who gets to do what with her, from bedtime to coats, you are giving her decision making power over the adults in her life and that is just setting yourself up for trouble later on - imagine her as a 12 year old or 16 year old if she learns to believe that she makes the rules and decisions for her parents...