Thanks everyone for your thoughts. I really do appreciate it!
First, my mom is completely awesome!!
: She was at both of my homebirths and is amazingly supportive!
Second, just a bit of an update: my mom took her and dd#1 for about four hours yesterday afternoon and I went home to sleep. Managed to sleep for about two hours so it was a nice nap. I find myself to be such a light sleeper these days that any noise wakes me up instantly and I'm on hyper-alert. Sometimes I swear I hear my children breath even when they are miles away.
Also, dp usually has to get up for work extremely early and he works a relatively dangerous job so I've always been the one to get up with dd. He didn't have to work today so he actually got up with her and i got an additional two hours of sleep this morning. That was heaven.
I know things will get better. I have a five year old who *usually* sleeps through the night and time really did fly, so I know it'll all be better soon enough. HOWEVER, I agree with HANNAH32 that sleep is biologically necessary. Perhaps we don't need the generic (mythical) 8 hours a night that people talk about, but I know there are scientific studies to support people physically needing sleep. I know for me, personally, I feel foggy and I don't "connect the dots" as well during the day when I don't get sleep. Not to mention, I'm a mean ole bitch.
I think for now, I'll keep having my mom take the girls whenever she can during the day so that I can nap and revisit this idea when dd is a bit older. In the meantime, I've got to figure out how to get her to sleep for longer stretches.