Stay at home parents, given the opportunity to work again in the corporate world or abroad with a really competitive salary, would you leave your kids for it?

No. My previous employer offered me to come back and work again with them. The salary was more than 2x my last salary with them, and the benefits were great. But I declined and chose to take care of my child. Aside from the fact that it is very hard to find a trustworthy helper, I would want to be present during my child's formative years.