I have had 2 kids as an undergrad. My oldest is 5 and my youngest is 2.
It is certainly doable!
I usually do all of my studying after they are in bed for the night and some on the weekends when my husband can help out a bit more with watching them.
As far as not getting any sleep, you actually kinda just get used to it....lol
So far I have been able to work it out where I take most of my classes in the evenings (have done some online) so I have no daycare expenses and am able to spend all day with them.
I just have to prioritize my time more but its really not that bad. My youngest still takes naps so I use that time to study as well.
I take about 15 hrs a semester and pretty much make all A's.
M