Wow, we are in a very similar situation (age-wise).
What state are you in? (Curious about that program you mentioned).
When I begin my pre-reqs he will be in regular school (kindergarten), so I will have him covered from about 7 am - 6 pm (with the after school care program). I will be doing my pre-reqs during evenings and weekend. I have to work full time as well and I have a really great, really flexible day job (not a career, but it's a job). The school I'm going to offers evening and weekend drop off care for student (can you believe that!). So, I'm taking advantage of that.
He will be about 7 or 8 once I start a nursing program. That's the part I'm not sure how I'll work it out. I have to work to pay for living expenses (rent, electricity, car insurance, my son's school expenses, etc. etc.). I'll have to take day time classes since nearly all nursing programs
here are offered during the day (unless I can find an evening program that also offers child care, fat chance, but I'll keep trying). I'm trying not to let it stress me too much because you never know what my situation will be like 2 or 3 years from now. There's no telling what new resources will be available to me at that time. Maybe I'll befriend some parents at his elementary school and I'll find child care help that way.
I don't think financial aid and loans will cover all of our living expenses. We live in NYC. It's super expensive to live here. Hell, a good paying job barely covers minimal expenses in NYC!
I'm terrified, but confident.