You are between a rock and a hard place. I would take up anyone that you can to take your daughter, even if it means waking her in the middle of the night and dropping her off. First of all, kids are resiliant and she will make it if you have to do this. Second, you need to focus on the birth of the new baby so it goes quickly and smoothly & you can get back home.
My husband stayed over night with me in the hospital for our 1st. For our 2nd, soon after the baby was born, he left and picked up our toddler and brought her up to the hospital to meet her new baby sister. They stayed for a bit and then my hubby and daughter went home for the night and came back to get me the next day.
Hopefully that baby will come fast (my 2nd labor was MUCH longer...10 hrs compared to 5 with the 1st) and your husband can pick your daughter up soon after.
Best of luck!!!