I am unable to log out of all sessions involved with xbox

Thanks, however I am not sure of what you mean by "Home Xbox"

We have one Xbox in one room and another Xbox in another room.

We both have Xbox Live Gold Accounts.

On the Xbox that she plays on, does not have me logged in

On the Xbox that I play on, does not have her logged in.

If I log into my Xbox first and start playing, then there is no issue

If my wife logs first (on her Xbox) in or has not logged off the last session, then I am unable to start a game.

Same. I can't sign into the app on my phone and it's making it impossible to obtain my points for completing a rewards offer involving said app. I logged out & logged back in to see if it would fix the processing problem with the reward, but instead I'm
stuck logged out, unable to do anything. When trying to log back in it takes me to a non functional website.

ive done this and am still unable to join games sessions

So, does that mean I really cannot do anything? Or will I keep getting hacked until the person stops hacking me?

Oh, I see. It can only be logged out if you can access the account on that specific device.