Whilst I don't have children, I do have a full time job that occasionally involves long commutes, dogs and am studying for a degree which is approx. 20 hours of study a week.
On top of that I have other commitments with family. Often involving ferrying to medical appointments etc.
In all honesty, OP, the only way you do it is to be absolutely tight on timings and dedicated to getting the work done. You also look for ways to double up on times.
For example, on a long drive I can get an audiobook on my degree subject to listen to and use the time to learn and think about assignments etc.
When working I almost always use my lunch hour for something else. If I am working in an office I listen to lecture recordings and make study notes. If I am working from home I fit a dog walk in then.
There are 168 hours in a week:
If you spend 45 of them working/commuting, 56 of them asleep, 12 of them studying then you still have 55 hours left to take care of your family and yourself. It is possible.
I also work in a job I do not love and am studying a subject I do. The reality is my job pays my mortgage and so it is critical that I do a good job for the security it brings. I would love a world where we all get to do exactly what makes us passionate but the reality is often different. Having to perform a dull (to you) job to a satisfactory level is something many of us have to do.
If a job in Tesco is what you have to do to keep a roof over your head and food on the table, while you study to be a midwife then it's what you have to do.
I totally understand life has handed you all your challenges at the same time and think some have been overly rude on here. However, life is not fair - for anyone. There are jumps you have to get over to get what you want. They are doable but only you can answer whether or not the end result is worth the pain, to you.