I think I'd just stay single
These other posters DO make a good case. They really do. I am not as bitter as some others. At least not every day!!
So.......do not marry her.
So......enjoy her company, her cooking, her oyster.
So......now, you are in the drivers seat. You see her, or you don't. You will have the best of both worlds...for a while.
So......she will use every feminine wile to get her ring back from you. Enjoy her effort....while it lasts.
So......see her when you get lonely. Seeing your kids would be nice. I love kids...do you?
She threw away your marriage. Let's see if she can muster another dude to haul her ashes with five pretty children in tow. She might find another man. He will not be as good as you.
Keep her as a friend with benefits, nothing more. That is likely what you are to her. Do not tie up your finances with hers. Pay your child support only. Buy the kids gifts if you like.
Bring groceries over on occasion. Take them all out to eat at some kid friendly restaurant.
This I guarantee, this women will reward you ten-fold until she gets you to re-marry her. That day need never come. Treat her REALLY NICE.
Again, this is if you really like her. AND
,if you can pull the plug sometime down-stream. Pull the plug and let her boat sink for good, if she misbehaves.
After a year or two, you may tire of her. Then find another women to make your wife.
On reflection, this is a better option. This will be the best wake up call for her.
She dumped you for a rich handsome guy. You string her along for a year or two, never marrying her. At some point in the not so far out future, you tell her goodbye. She will force your hand, anyway.
But, this is bad advice. It will take nerves of steel. If I lightly tap your head with a wrench.....will it go clunk?