She's 4, she misses her mom. She'd miss her dad if he was gone so much too. Maybe you can carve out some one on one time with her. With my boys I read 2 books and have a 5 to 10 minute cuddle every night.
Maybe if you make some "girl time" before bed things will go a little better. Make it fun, wear tiaras (you can get cheap ones a party city) read princess books, tell daddy "No Boys!" (you can always ask the princess if prince daddy can come in for a kiss at the end). Then tell her if she throws a tantrum or doesn't stay in bed you won't do this with her anymore. If she cries when you leave, tell her you have to do (fill in the blank) and when you're done you'll come up and give her a kiss. My son is always out cold by the time I come back. Piggie back rides always help me get them upstairs too.
Just a thought.