Upvote:3
I thought that maybe we could buy the tickets in her maiden name and use her passport that matches this name. Could this cause any problems?
Anything can cause problems, but this is unlikely to. With a passport and a ticket in her maiden name, how would anyone know that it is no longer her legal name? Certainly nobody will care that your names don't match; it is hardly unusual for a married couple to have names that don't match.
(Immigration officials will sometimes even accept a passport in an old name in combination with a document showing the name change, such as a marriage certificate, but these days airlines are far less likely to do that.)
Do bring the marriage certificate just in case. It will be particularly useful if she has to show her driver's license (or any other document with her new name) to anyone.