Lila -
I have to agree with OT here.

And maybe this will be the opportunity to sleep train D (I don't understand why you keep putting it off? Now you're gonna wait until you move in with your mom? Why? Wouldn't it be far better to get it done BEFORE you move in with mom?)

I'm worried that maybe the reason she sleeps when he's there and not with you, is that you DO give off a worried vibe when she wakes up. Try staying in a firm, calm, HAPPY space. No need to reassure her - I think you super-impose your OWN worries onto her. Consider this a chance to have a whole week of very consistent scheduling.

If she sees that life is happy and fine without dad there, and his being gone for a few days is NO BIG DEAL, then it won't be a big deal. My ex traveled for business a lot when we were married - my kids never batted an eye, because I never made any kind of deal out of it. She will take her cues from you.