Brands of Engine Mounts?

[Poodle]

If one mount has gone they probably all need replacing - as it happens the gearbox one causes gearstick movement and the top mount can knock when it's really tired, so sounds like they're well gone anyway from your description. It'll make a huge difference to handling, the engine is a heavy old lump to be shifting around in the chassis as you corner, could well be an underlying cause of your handling issues.