Hello K.,
I am sort of in the same situation as you and your daughter. My husband has been working a lot of overtime. He leaves before we get up and comes home when we are in bed. He works in the AeroSpace business and can't say no to the overtime. I can tell the change in my son's attitude, by the way my son is 3yrs old as well.
So, we try to call Daddy during his lunch hour, which is is normally working through. If we don't reach him, Dean leaves a message. Dean also colors pictures, paints, makes little notes and we put it in Daddy's lunch bag the night before.
Maybe your Daughter could mail her Daddy some art work, I am sure she would love to do that and her Daddy would appreciate and love the stuff she sends.
Don't know if he has access to a computer, but do a webcam talk every other night or day if possible.
Don't know if the place where your husband is has anything fun for a 3yr old, but when you make the trip out to see him, maybe go a day early or stay a day later and do something fun with the kids and stay in a hotel so you could do dinner that night with her daddy.
I know it would be hard on you as well, but let one of the days that you go and visit him to be just a Daddy and Daughter day, or let him take her out for ice cream or something, just give them some alone time.
Oh yeah, make a calendar and let her (maybe when she gets upset) mark off the days till Daddy comes home.
If you have a Video Camera your daugther can record a message and mail to her Daddy and if your husband has access to a video camera he could do the same.
Just some ideas, well my son is yelling he wants to go outside so I better go.
Good Luck and how your husband comes home very soon,
M.