Scott, what makes you think your W will actually use the $$ to take the kids to the park?
If I were you, I would go pitch black, except for the kids, and do not give her any more cash. Pay whatever bills yourself and stop enabling her. Act as if her divorce idea is good for you too. Stop trying to woo her back right now. Also, I wouldn't send her a letter of any kind. Do not put anything in writing. Just watch it play out and let her crash and burn.
Also, please go for custody, or at the very least, shared custody of your kids. She is damaging them and it hurts my heart to read about how she treats them.
This may actually have the added bonus of making OM see how desperate she is. And all addicts are desperate.
P.S. I was just marveling at how your W can't be your friend, wants a D, rubs OM in your face, and then has no shame in pestering you for money all the time.