No, bring it along, just in case she wishes to rent a car somewhere. When traveling overseas you can never have too many documents.

Here's what I'd do: (1) Passport is sufficient proof of identity at official places like Immigration, Customs, etc., so just use the passport. (2) If renting a car, etc., where a DL may be required, just use the DL. (3) In case there is a situation where she has to show both Passport and DL, have a copy of marriage certificate handy. Just don't raise the issue yourself. In fact, never raise any unnecessary issue with any bureaucracy anywhere.

When the trip is over and there is some quiet time, she should change the name in the passport. Keep the old name as "alias" or whatever the procedures allow.