Messages in macOS Sierra incorrectly sends (back) to my account; works as intended in iOS 10
I had this issue and your solution didn't fix it for me. It drove me nuts. Deleting my Messages database is what eventually fixed it (note: your message history will be gone on your mac but still available on your iOS device):


In Messages.app , go to Preferences -> Accounts and sign out.
Quit Messages.
Kill the IMDPersistenceAgent process via Terminal with killall IMDPersistenceAgent^
In Finder, use the key combination Command-Shift-L to browse to the Library folder
Rename 'Messages' to 'OldMessages' (I didn't want to trash it but you can if you like).
Cleared the preferences cache by running killall cfprefsd in Terminal^
Restarted my mac
Opened Messages again. I sent a test message, and this time my wife received it (and I didn't).


^Commands came from this article

UPDATE
I had this issue again today (2017-08-09), and again the steps above cured it for me at the cost of losing access to my message history on my MacBook. Curiously the issue appeared after upgrading the iOS version on my iPad (whereas the issue occurs on my MacBook; my iPad has never exhibited any messages-related issues). 

I tried @brian-m's suggestion of moving the OldMessages folder back (after steps 3 and 6 above); sure enough I can see my old messages just fine but the original problem is immediately reintroduced. So it's some sort of database issue. I had a bit more of a poke around and can see it's a SQLite database. There's a good discussion of the schema here. Unfortunately I don't have time to delve further.