I've had 50/50 custody with my 6 year-old daughter for a year now. I do feel for you, but you do need to deal with your response to her leaving for your daughter's sake. Being emotional when she leaves is affecting her and will lead to issues. (I've seen it with my now grown step-kids, as their mother made an emotional issue of each leaving).
Not every family can do this, but our schedule only has her away from me for 2 or 3 days at a time (week 1 with me - sun, mon, tues, fri, sat; week 2 with me - tues, wed).
We also have webcams at both houses (about $20 at Target or Best Buy) and she knows she can ask to "visit" over webcam anytime. At age 6, phone calls are becoming more possible, too.
Her Dad and I send emails to each other about what she's doing, not every day, but often. We put "cute Raine story" in the subject line so we know it's not about an issue.
And yes, stay "busy", but more than just busy - think about what you can do with your time that you find rewarding, that you wouldn't be able to do except you have this time free - and do it.