Should I ask my exwife to reconcile?

In matters of the heart, you never know which way the pendulum is going to swing. You shouldn't try to win her back. That is just going to prolong the situation. If you love someone, let them go free. Make yourself available only when the children are involved. Absence really does make the heart grow fonder. Give her plenty of absence. It's a girl-trick, but it works. If you're talking with her on the phone, and the kids have been discussed, get off of the phone. She knows you love her. It's gonna make her wonder if maybe she made a mistake. Give her all the absence you can. To 'win her back', you've got to ignore her. I know, easier said than done. But it has a better chance of working than anything else.