Arriving BACK at the US should not be a problem.

Not only did my spouse have this issue for some time, especially since several European countries (and others) do not have spouses change names, but several friends and extended family as well.

The biggest issue was ALWAYS the "hired" "security" goombas before "real" check-in, airline employees doing the check-in or boarding verification-basically front line airport staff. CBP never once blinked an eye or said a word about it.

I guess I should say YMMV, but in my experience with it and those I know it always eventually worked out.

But of course the issue is getting into Mexico. Not having the marriage license is a bummer, but I suspect it should work out. You could e-mail/call the nearest Mexican Consulate and ask them as well.

To the suggestion of changing passports; some countries will not do that since women (or men...) do not take spousal names. Some will add an amendment in the passport noting who the husband is (Italy, for example, will do this).

My advice: Try online check-in and get to the airport early...