OK, so first off, you're a good egg sir. I recognize the internal struggle you're having, I've been there myself. A lot.
Now, that said, I'm gonna be a touch harsh.
Everything about this situation, to me, screams that there is a drug issue. I've seen it way too often. The abusive (but now returned) partner, the seeming constant (and escalating) need for cash. There's every possibility that any "support" you are sending is being spent on an addiction. Possibly for both her & the abusive partner.
Here's the thing, it isn't on you to "fix this". IT IS NOT. Unless you truly, fully want to, and these things get very hard & dark very fast. Again, been there. It sucks. And often, you don't "win". Drugs are awful adversaries.
I hope it isn't this, but the pattern is all too familiar. But here's what sucks. If it IS a drug habit, those kids are in danger. And if you report it to get the mother help, it could potentially mean the kids get taken away. Which... well, its not good. They're out of one shitty situation into slightly less shitty one.
I've had to do this before. In the end the kids got taken away, the mom relapsed & overdosed, I lost track of the kids (the system basically told me to fuck completely off as I had no rights to know what happens to them). She was an old friend from high school. Anyway pal, I really feel for ya. Seriously. If you want to talk, just hit me up. Sometimes an ear can be a lifesaver.