One semester is a finite period, so difficult or inconvenient arrangements should be tolerable in the knowledge that it's not long-term, and essential to your qualification. I'd go solo, but with fixed plans to alternate travel at w/e: one weekend you travel, the following one they travel. (Or at a 2:1 ratio, with you travelling more frequently than your husband and daughter). Make it an adventure for your daughter, or she'll pick up your cues about it being emotionally challenging.
I have had to say no to so many unbelievable opportunities during my children's early years (that dads with supportive partners would've taken up in a heartbeat), that I've become evangelical about women doing whatever is necessary to access fully those opportunities that will define their future careers.