Yeah, binding myself to this person again financially and legally would be a really dumb move, I definitely see better alternatives now.
Are you ready to get remarried - to her? If not, then don't entangle yourself into co-ownership without the legal protections of marriage. A few hypotheticals for you...
- your ex loses her job. You're on the mortgage, and now you're responsible for the full amount. You good with that?
- you don't want to, or can't, pay both halves, so your credit score absolutely tanks. You good with that?
- meanwhile, she remarries, and you can't stand the guy. He's living rent-free in the house you're paying for. You good with that?
- your kids grow up quickly, as they do. You still have 20 years left to pay half her 30-year mortgage. You good with that?
- you remarry. Your new wife wants the house sold asap and your commitment of now-joint funds terminated. You good with that?
It's commendable that you want to help your kids. But either the place she sleeps right now is "enough" - truly adequate shelter - in which case your kids are fine, or, if it is truly inadequate as a shelter, that's for the courts to sort out in regard to impact on physical custody and visitation. I'm going to go out on a limb and say where they stay with her now is good 'enough' and I think you are FAR better off (as the person in this equation that seems better prepared, financially, for the future) to save, save, save for college, so you can launch your kids as debt-free as possible into the world. THAT would help them tremendously. A fancier place to rest their head at night? Seeing what happens when you don't handle money well is a very good motivator and could put them on the right path for life.