By now I experienced several times of losing my mouse pointer after using the chat.
(I made sure there was no blinking cursor in the chat input box - so no focus issue.)
So far I tried pressing [ESC] several times and using [Alt]+[Tab] to switch out and back into the game. Didn't work.
As a result, I was stuck with the first ship on my bar to enter the fight with.
To prevent this you should of course make sure you've picked an appropriate ship prior to using the chat on that screen...
But it would be great if this could be investigated. Chatting with your team could result in wanting to pick another ship - which by then might not be possible anymore.