I don't know if the attitude should be "teach her a lesson". Sounds sort of harsh, but yes, I think you have the right mindset. There are emotional reasons to work it out and practical reasons.
It's sort of like I told a friend....it doesn't matter why you get a job....it matters what you do when you start working.
In this situation...it doesn't matter why you stay together and work on it...it's what you produce in the new relationship. If you stay together for financial reasons at first, but then turn this marriage into a solid rock where everyone is getting what they need and everyone is contributing what they need, all are happy....so be it.
