Since I've been trying to finish college for about 17 years and I have four kids ranging from 2 to 14yo, I've pretty much done it all.
In-class with a newborn...didn't work.
In-class with a 2yo...it was okay (one class at a time).
Televised (watched from home) with a newborn and a 4yo...it was okay...even the time I took 4 classes (and finished 3!).
Online I've done with a newborn plus two older kids plus a WAHM gig. It was fine but I didn't take more than 2 at a time and it was easy, just do-able.
The past year I've been doing 2 classes at a time (attemped 4 one term and it didn't work!) with a 2, 4, 10 and 14yo. I do 90% of my work late at night when the house is quiet. I dropped my WAHM gig mostly last fall and haven't spent any time on it (I'm a freelance photographer) really.
The best thing about a newborn is that they love to sleep in the sling and that works out really well with online school.
The other kids are harder to keep happy/entertained. I've considered hiring a mother's helper (or paying my 14yo to work for me a few hours per week) -- is that an option?