On PC, I've found the quickest and easiest way to fix this issue is to ALT+TAB out of the game and back in.
However, it's extremely annoying because, as you mentioned, you don't notice this to be an issue until you are in a "vehicle" and can reoccur.
I got this issue alot of times.
The easiest way i found to fix this is to spam f1,f2,f3,f4 fast a few times. i dont know which one does it.
But this fixes the issue for me so i can move the mouse without it lagging and without shooting like 10-25% of the speed.
Like I mentioned before, the easiest of all tricks until they fix it;
Open and close console
This is done by using the "Tilt" key ( ~ ).
Hope that helps.
