Chris -

We really need to know which Volvo model you are asking about.

On a 240 it's easy to check motor mounts. So as to avoid a burn, do this with engine not too heated up. Use a hand under the oil filter to check clearance downward to RH mount. If filter is too close for finger to fit, mount is bad.

Front mounts are such that on a collision the engine can move rearward AND drop down thus staying out of passenger's lap. The front mounts are at an angle so the engine/trans unit wants to move rearward. They are held forward and up on that angle by the transmission mount. The trans mount is the first to go - it's back there with oil leaks, road salt and crud, chemicals that splash up when you go through a puddle of whatever, etc.

When the trans mount weakens, the engine/trans unit begins to move rearward and the motor mounts cannot resist. They fail, too.

You say the shifter handle moves when braking, right? What direction, front to rear or side to side? I suspect the former. Why? The momentum of the engine/trans unit wants to move it forward under deceleration from braking. If it moves, the movement can pull on the link between the shifter lever on the trans and the rod/handle in the cabin, thus moving the handle, probably rearward.

This is probably more than you ever asked to know. Just my 2-cents worth.

Good Luck,

Bob

:>)