I handled it by divorcing my now-ex-wife -- and I don't mean to be cavalier.
Let me explain. I worked full time, put $ in the 401 K, the kid's college fund, paid the mortgage, etc. Wife worked part time as a nurse.
She came home, dropped the bomb, said she was moving out. At one time she offered to just separate, but she wanted to explore this R with the OM who lives 350 miles away. Thank you, no.
We worked out a deal where I have legal custody of our three girls and retained the marital home. What was devastating to me at the time was just how easily she signed legal custody of her children away to me.
I paid ex a chunk of cash as part of the settlement. As long as ex lives in same school district she is entitled to have the girls roughly 50% of the time. If she were to move away to move in with OM, I would seek child support.
Ex is now working 60+ hours a week to make ends meet and scrambling to pay her mortgage and other debt she racked up. She hooks up with OM every other week or so. It's really pathetic.
Just this last week she asked me to help with her portion of the youngest D's preschool payment. I suggested she seek support elsewhere. Please note I'm not DB-ing or trying to bring her back into our M.