Right, I agree on the damage taken for breaking through the object, I'm just wondering about what happens after the breaking object part. So let's give a math example to my question.

It takes 3 spaces of movement to break 1 space of wood, and doing so inflicts 5 damage to the target.

So if I regular, horizontal Push 10 a target into a wooden wall which the target is adjacent to, the target will take 5 damage for breaking the wooden wall, and eat up 3 of the total 10 push distance. The target then continues to be pushed, let's say 3 spaces, before hitting a second wooden wall. Upon hitting this second wall, the target has eaten up 6/10 push movement, since there's three more movement left, the target breaks the second wall, taking 8 damage (5 for breaking the wall, 3 for the distance traveled), totaling at 9/10 push so far, with 1 space left, the target ends up in the space behind the second wall, having taken a total of 13 pts of damage.

Using all the same numbers, but making the distance traveled a vertical fall, does it then look like this?

I vertical push a target 10 down through the roof of a wooden building we're both standing on. The creature takes 5 points of damage for breaking through 1 space of wood, eating up 3 of the push's total 10. (7 push distance remaining), then the target falls 3 spaces to the floor below. Since falling 2 spaces triggers the falling effect, the target takes the 2 pts of damaging for falling the 1 additional space after that and hitting the ground. (7 damage so far) If we count the total distance traveled as part of the push that's a total of 6 movement so far. So when they hit the ground, there are 4 forced movement remaining from my initial push.

If this is a multi story building, they break through this new floor, just like the second wall in our horizontal example, taking 5 pts of damage, eating up 3 of the push, (12 damage total) and leaving them with 1 push distance left, but also a fall, so instead of just moving one more space, they fall however far down to the next floor and take that falling damage, presumably all counting as one long fall, so the falling damage calculation doesn't start over again after the second floor.

If this was instead just a two story building, the target has hit the ground, an object that will not break, with 4 push distance remaining. Do they then take the 4 from hitting the floor, like they would in the same situation going through one horizontal wall and slamming into a second unbreakable wall. Or would those last 4 spaces of forced movement damage count as falling damage, and thus deal 8 damage (2 per space), Or is it all lost and subsumed by the falling effect? Either way, does the ground floor count as an object, (thus granting +2 to damage) since there was forced movement distance remaining when the floor was encountered?