yes, this is very normal. we have the same issues in our house.
I honestly feel really badly because both kids want me when I'm around, but my husband does almost all of the heavy lifting day-to-day (taking the kids to day care and back, doctors' appointments, etc). His work schedule is much more flexible than mine, and I feel like I've really dropped the ball.
Have you considered just not giving her the option? We have an every-other night routine with our kids. Last night was Mommy's night with our 3.5 year old. Tonight will be Daddy's turn. We have different things we do with them.
I'd also suggest starting a Daddy/Daughter day once/week or every other weekend. Just something special the two of them get to do alone - go to the park, go to the library, go to Starbuck's and draw together.
Soon, it will change, and they'll prefer him. It's all cyclical in the end.