Account, paid for Apps and new account
Could you ask your ex-wife for the password? That would be the easiest way.

If that doesn't work, you could start a password recovery procedure on a PC, in some cases it uses a registered Android device to verify ownership, which you have access to. Just click on the "I forgot my password" link at gmail.com.

Sadly there is no way to transfer paid apps and in-app purchases between Google accounts.