An infinite mass is impossible. But in any case it just limits the usefulness of that frame.

I believe the correct approach is to look at it from the perspective of the object that you in car A are striking. Taken from the perspective of the wall, car A strikes it at 100mph. From the perspective of car B, car A also strikes it with the same speed (and kinetic energy).

IF the two cars have equal mass, this will also be the impact energy on car A. And that’s what we’re trying to find for both cases.

> I believe the correct approach is to look at it from the perspective of the object that you in car A are striking.

The most convenient reference frame for colliding objects is the combined center of mass of those objects. It isn't affected by the collision, and for perfectly inelastic collisions the objects will come to rest with respect to that frame. This makes the math a lot simpler that working in some other frame.