I would approach this shot by first stabilizing the shot so that the garage door's upper right corner does not move. Just put a tracker there and then stabilize.
When that is done you should be able to lay a still image of the garage door over the shot and perfectly line it up. Use rotoscoping to create the mask of the actor moving in front of the garage door and take some time with layers to fix the open garage door visible through the car window.
Now add a null to the shot, move to the first frame of the shot, reveal the Anchor point property of the original footage by pressing A, then create a simple expression using the pickwhip to tie the null's position to the layer's anchor point. Now parent all of the layers, the original footage and the garage door and any other layers that are part of the shot to the null. The camera motion will return to the original shot and the garage door will track perfectly with the rest of the shot.
Here is an example that uses the stabilize, add a layer, and then remove the stabilization technique to position a target over a flautist.
Sorry there is no audio so read the captions carefully. The pre-comp would be your garage door.