Extended travel with family members of mixed citizenship [closed]

Background: My wife is Canadian, my kids and I are US Citizens. We've traveled a bit internationally (mostly to Canada and the occasional Caribbean trip). We are planning years of extended travel in 2018. Starting with Canada, Mexico and then Central America, ending in Panama and then onto the Galapagos and various other places. All members have passports and major US ties (rental property). Wife has a 10-year green card with 4 years left.

Question: What are the advantages / disadvantages of us starting our travels without her US citizenship? Does it really matter? She intends to become a US citizen at some point, but it hasn't been a priority in the last 11 years. It would be nice if she could vote. It would be nice to NOT have the green card expiry hanging over us.

Some of the things we're planning on doing are considered high physical risk to some - though fairly normal to us. Aside from a major international crisis, what are the reasons we may want to do this or not prior to leaving? Situations you can imagine this being an issue especially in countries mentioned? Here's a situation: What if all of our travel documents were stolen? Would we all end up at a different consulate than her? Or, say we were accused of doing something illegal in one of those countries. Just playing the what-if game here.

Additional Details: Travel will likely be for 2-3 years with at least 1 visit to the US and 1 to Canada per year, but likely more frequent to see family. First marriage (for both of us), yes kids are US Citizens and do NOT yet have duel citizenship.