You could have put her to bed every night and she may still have developed this issue, or she may have needed Daddy to do everything and not wanted Mommy to do it.
I travel a lot for work, and while I'm gone my husband says my daughter is "a real cupcake", but there were periods while I was home that she wouldn't let him do ANYTHING for her, and could throw a real tantrum about it. She's almost 6 now and things have been far more balanced for a long time.
I can tell you that it is no fun being the recipient of all the attention and needs, for 1, you feel guilty and you feel bad that your child isn't expressing their love for the other parent, and 2, you get stuck doing everything for them or having a battle, both are exhausting and frustrating.
Mostly, all you can do is wait out the phase. Know that your daughter loves you as much as she loves her mother but for whatever reason she wants mommy to help her. The things you can try, are having you and your wife tell her that the 3 of you are a team, that sometimes mommy will put her to bed, sometimes you will, and you all need to help each other out (this applies to all tasks, but bedtime is one of the toughest). Your wife can take the occasional night off and go out - which might do her good for just mental health as well - but this will probably only improve the situation on the nights she is gone. Hang in there! As hard as it is for you to feel rejected by your daughter, your wife is bearing far more guilt plus the entire burden of her care. Your daughter loves you and will grow out of this phase eventually. If nothing works with the bedtime routine, take on as many of the other tasks as you can, getting her dinner ready, giving her a bath, whatever you can do. It will give you some bonding time with your daughter and it will show your wife you are trying, BUT for the record, there was a period where my daughter would not let my husband do ANY of these things if I was around - I would have to go for a walk or to the store, anything to get a break. Just make sure, if you resort to those, that you and your wife don't tell her "see, you made mommy leave" :)
You didn't do/not do anything that made your daughter behave this way, and you probably are not going to do something that miraculously improves her behavior. You could try coming up with some new activity that only you and your daughter do, "a special daddy-time treat". Just don't feel too rejected if it doesn't always work.