Oh, that stinks.

On the feeling like a crappy intern front - as comes up frequently in these threads, I think that's nearly universal (goes up and down during the year, but everyone feels it much of the time!).

On the not seeing your daughter part... blech. Is there any way her bedtime can be shifted? Can she sleep later in the morning, or do childcare arrangements prohibit that? Can her nap be pushed later, or extended somehow?

On the social part - I go through periods where I prioritize remembering to have an adult social life, but a huge amount of the time these days it's something that's just on the back burner. I try not to let my long term friendships totally wither - ok, they're pretty withered, but not totally die - but I mostly accept that making new connections that are as strong as the old will, for now, be limited to people who understand my situation and are willing to tolerate limited contact, with kids present at every social engagement I go to, always. And I spend most of that time interacting with my daughter primarily, and the other adults secondarily. Right now, I feel ok about it.

Also - the refrain of intern year - it WILL get better!!!!

DocE-
If it makes you feel any better I could've written your post. I have around 100K in debt and I think about quitting on a daily basis. I'm in pathology right now. I've come to the conclusion that I need to switch specialities. The lifestyle is decent (I still consistently work 12 hours days) but I've found the pain of medicine too much without the warmth of patient interaction. I wish there was a solution for people like you and I, but I haven't figured it out yet. Just want you to know that you're not alone.