Does my umbrella cover me overseas?
Generally for incidents while traveling, yes. Living abroad is a different question, because many policies require the named insured to reside in the United States. If an assignment takes you out of the country, that is worth raising before you go rather than after.
What about driving while we are posted abroad?
Your United States auto policy does not operate overseas and the umbrella above it follows. Cover has to be arranged locally wherever you are. That is true generally, not only for Mexico.
Should I keep the policy while we are away?
Usually yes, particularly if you still own property here, and the terms need checking against where you will actually be living. We would rather set it up correctly in advance than work it out from a different time zone.