It took me a while to figure this out, so I thought I'd post the solution here. Surely I'm not the only one to come across this...
When using mouse or touchpad control during game play, the character can only rotate, at most, 180 degrees. This is because the curser is hitting the edge of the screen and the game stops receiving mouse signals.
To solve this:
go to "Run Windows Application" -> select the bottle you have installed GTA3 in and type regedit
navigate to HKEY_CURRENT_USER/Software/Wine/gta3.exe/DirectInput ... if DirectInput doesn't exist, create it by right clicking the key "gta3.exe" and selecting new -> key. create a string value called "MouseWarpOverride" (without the quotes) and set its value to "force" (again, no quotes). Exit out of regedit. Run the game and... voila, Buddy can rotate 360 degrees!