I'm a single mom of 2 little girls, my youngest will be 2 next week & my oldest will be 4 in Dec. I work 30 hours a week and attend graduate school online. I was a SAHM until my ex & I separated, then my girls had to go to daycare for the first time. I've had so much guilt over that. But they've adjusted wonderfully. I've taken a lot of grief from my ex about my choices, but I know that I--and consequently my girls--will be better off in the end.
You may want to consider taking at least one class online or going to school part-time, not only to help relieve some of your guilt & frustration, but because you're likely to burn yourself out doing so much. If that's not an option, just make the best use of the time you have with her.
Also, lots of parents work the night shift & what else would a person do if they didn't have family to help? You're lucky that overnight daycares actually exist. And it's just 3 nights. If she's adjusting well I wouldn't worry too much about it.
You don't want to have to work this hard forever so if you can do it now, I say go for it!