I wonder if you could somehow manage to finish your degree. What concerns me is you describing lack of funding for research, which seems necessary. I guess you cannot finish your doctorate in an institution that has more to offer?
Anyhow, I know how you feel. I only have one child, and I am still with his dad, but I did go back to school to do a master degree at the Royal Conservatory in the Netherlands. The baby was 8 months old and up every two hours at night, we were in a new country, having to learn a new language, and struggling not only with culture shock but also with very extreme weather. (Until two days ago we still had snow storms and icy winds, felt temperature of -15 degrees celcius), and a many months with only a few hours of daylight. My husband suffered from severe depression for a long time, and had a hard time finding work as an immigrant. We hardly had enough to eat for months, getting skinny and feeling even worse. But we worked through it. I wanted to quit my studies many times, but my husband did not allow it, saying I would regret it forever. The pressure from the conservatory was huge too, and I ended up very lonely and isolated, doing nothing but being a mom, the household, the baby, school.
Now I am 3 months away from finishing, and I feel great. The last couple of years were horrible in a way, but I did it. My husband finally found work, and even though we are still broke, we have enough to eat now. I have learned so much in school, and feel a confidence I did not have before. My son will also benefit from this, watching us struggle through hard times, never giving up, and finally getting to where we need to be. (He did always have enough to eat by the way. He's been doing great the whole time.)
So I wish for you that you can finish, for yourself, but in the long run for your family also. Once you're done, you're done. You'll have a degree that no one can take from you. Good Luck!