You need to sleep, mama. Sleep deprivation is serious! It makes people crazy, literally losing-your-mind crazy. Falling apart, as you put it....You're no good to your babes if you can't function.
I left hubby and kids, no backwards glance, picked up some "fridge friendly healthy food," rented a hotel room and slept for two straight days, only interrupted to eat either my good food or room-service yumminess.
Then I went home and put in ear plugs at night for the next 3 months, leaving hubby in charge. Was it easy on him? Were there moments my kids *needed* me? But six years of extended periods of NO REM SLEEP left me incapable of anything else.
Years later we're all okay, but I remember that time. Love your family and love yourself... and take the time to bring yourself back to functional. And know that you're not alone.