You need to deauthorize ADE first, ctrl-shift-D.
Then authorize it with your new ID; menu/Help/Authorize Computer (menu/Library/Authorize Computer on the older, more reliable ADE v1.7.2)
Depending how you use books and devices, you may find it most convenient to share an Adobe ID with your wife.
That way you will be able to share DRM books.
If you both already have books registered to different IDs that won't be practicable;
also if you want to use more than 6 devices/computers between you.