Would a second layer of housewrap cause problems?
There is no problem with doing this. Housewrap is "breathable" by design so you won't trap moisture anywhere. You could build a wall with ten layers of housewrap and it would be more durable, not less.

Regardless of how many layers you have, it's critically important to make sure your windows and doors are properly flashed to the outermost layer slash the one with the most integrity. When the installers complete this work, don't let them get away without re-flashing all your windows and doors to the new layer of housewrap.