How are the ears? I wonder if she's in discomfort and that's a contributing factor.
Not sure about taking her away - has she been away from you before? A new baby AND being away from mummy might be a bit much for her. You probably just want to be careful about too many chagnes all at once. I do feel for you though - you must be absolutely knackered. We've been lucky in that DS' sleep has been generally much better since he turned 2.

DS went through a long mummy-only stage, which thankfully changed by the time he was 2 (so also good timing with the pregnancy for us).