I'm in graduate school, work full-time and have a preschooler and an infant at home. I certainly do not ignore my children and I am very involved in raising them. Does it make me a tiny bit sad to drop them off at daycare when I go to work or class? Of course! That feeling reminds me that when I am with my children, it is about the quality of the interaction and cherishing our time.
I won't lie, it is very difficult. I am usually tired and the house is messy. I sometimes sacrifice day trips to the beach or a cookout because of needing to finish a project or having to work. However, there is always clean laundry (somewhere!), food in the fridge and diapers in the nursery. I do find time to take my kids to the park or visit with friends and I appreciate it that much more when I find the free time. I am so very lucky to have a supportive husband who isn't above helping out.
I've talked to several NPs who went through their programs with small children. All of them felt it was the right decision for them because their children needed more attention when they were school age. Yes, they are only little once....but at this age, there isn't homework, soccer, piano, etc. The kids are in bed by 7:30 and I can study a few hours before going to bed. I know when the kids are school age I will want to get away from 12 hr shifts and rotating weekends to be there for those activities. Being an NP will allow me to do so.
School, work and family is difficult to balance but feasible under the right circumstances. Caring for an ill parent or martial problems seems more important and it might not be the right time for you. School will always be there, in a variety of options--online classes or part-time might work for you. Your home life sounds like a priority right now. Good luck!