It is possible. People have done it. One of my nursing colleagues worked full time and raised 3 kids as a single mom while in nursing school, and one of my nursing instructors worked full time while in school too. For them it was a financial need that drove them. Nursing job = being able to put food on the table, so they had no other choice.
It will be hard but it can be done. You'll have to sacrifice time with family and friends, workouts and other hobbies. You'll have to be creative. I used to record lectures or record myself reading my notes, and listen to it to and from work or while exercising, and I had med cards taped to the kitchen wall to study while I prepared meals. I only worked part time though, no kids at the time, and it was still stressful and basically took over my life.
These evening/weekend classes, are they pre-requisites? If so you'll have to figure out what you'll do for actual nursing school. Most classes are during the day. There will be long clinicals too. Maybe look into what your schedule would be like and how you'll have to fit in work.
You sound really hard working and driven. It's great that you want to help others. Nursing is good for helping others but know you won't always feel like you're doing so. For example, I easily spend half my shift charting so the hospital can be reimbursed, and there are always difficult patients and families. But overall I'm very proud to be a nurse and am glad I chose this profession (also my second profession).
Best of luck to you!