Zenial,
I agree with everyone else that running is not an option. It sounds good in your head and solves short term problems, but opens up a lot of other problems. I know it's slow to go the legal way of getting what you want. But it's the best way to keep your kids.
I would document everything also. Even if it's small, Every little thing you can show a lawyer or a judge works to your favor. The more evidence you have on him the better. I know you said his mother is puppeteering him. Try not to focus on that, but your self and your kids.
Just take it one day at a time. Be strong and know that we are here for you. Have a great day.