It is difficult for young children to understand the necessity for the way adults rearrange their lives. Children crave consistency. I think it comforts them. That's why a child can watch the same video over and over and OVER until her parents are ready to climb the walls every time they hear the music :)
When something goes wrong in their lives, people look for reasons, and often people to blame. It sounds like your daughter is blaming her father for the fact that mommy has gone away. It makes no sense when you can understand the bigger picture, her father certainly isn't to blame.
I'm not even sure if she is old enough to be reasoned with in this. But I have found with my kids that when you bring these things out in the open it sometimes helps to ease or alleviate problems. I think they don't really understand what they are thinking or feeling, they can only experience it. They come up with reasons on their own, but often not the right ones. When you articulate the situation accurately for them, it helps them process better. This helped a lot when my daughter was having to adjust to her father being away, sometimes for weeks at a time. I asked her if she missed her daddy and if she was sad about him being gone, and then I told her that I missed him too and helped her find ways to connect to him even when he was gone.
You might try sitting her down and telling her that you are very sorry that you can't be with her during the day every day any more. Come right out and ask her if she is angry at daddy for something. Tell her both you and daddy are sad that you can't all be together all the time. When he is working he misses her, and when you are working you miss her. This may help reassure her that although she has lost your presence during the day she hasn't lost your love or your thoughts.
Then explain to her that sometimes you have to do things even if it is hard because if you don't you won't be able to pay for your house and your food and all the other nice things that you have. 4 is old enough to understand these basic necessities, even if she doesn't like them. Don't tell her she has to like it, or that she shouldn't feel angry. Share her feelings, don't argue with them.
Maybe you can work out some special "mommy time" that she can count on (do you have a consistent bedtime routine?) that happens even on days that you are working. My family likes to have occasional mommy-daughter or daddy-daughter days that are scheduled beforehand and not cancelled except for emergencies.
What are some of her favorite things to do? Help her father come up with special "daddy time" activities, maybe something only he does with her (to avoid having her comparing them with when she did the same thing with mommy). Sit down as a family to plan these (I'd suggest you plan both a mommy-daughter and daddy-daughter activity at the same time to avoid favoritism, with both mommy and daddy contributing to the discussion for both events)
My daughter finds it easier to cope with the fact that she is apart from me because she has a cell phone and can text me little messages when she needs to make a connection with me. When I text her back it reassures her that I am still 'there". Your daughter is obviously too young to have a cell phone but (assuming you and her dad have them) what if he occasionally lets her use his cell phone to "text" you (she decides the message, he texts). Or if not text messages, what about emails, which she composes, and he reads your messages to her? That will help her get over feeling that he is coming between you and her and will nurture the notion that he is her ally in staying in contact with you.
Now, to address her Dad's issues; he's probably feeling angry and rejected and hurt. His feelings need to be handled carefully as well. When you love someone and they seem to reject you it isn't always easy to understand or deal with the situation because your own feelings get in the way. It may help if he can understand that she is not rejecting him, it is only that she is looking for something to blame because she has lost some stability in her life. Make sure he knows that you are not blaming him for her rejection, because that will make him more defensive and aggravate the problem.
If you can make him a partner in finding ways to overcome her "childish four year old issues" he will be able to feel less rejected and blamed. Above all, don't set yourself up to be the bridge/conduit between him and his daughter. She is already used to just interacting with you (child <-> mommy), that connection doesn't need to be strengthened. But they can't be left to work it out with you out of the equation (child <-> daddy), because your daughter will feel rejected by you and he may be feeling too hurt to work effectively on the relationship. You need to develop the (child <-> mommy+daddy) relationship so that nobody feels excluded.
