Calling any theoretical physicist’s. Atoms travelling through time and space ideas

"But inelastic/inelastic is not really the answer, for even in an inelastic collision a reversal of traveling direction of necessity implies the object must stop, just before reversing direction. And if the object stops, of necessity the colliding object must also stop, for it cannot traverse the object."

That second statement is false, and not physics. The issue of being 'stopped' in this view seems to assert a preferred reference frame of motion, but we known from extensive experimentation, actual physics in this world is invariant to uniformly moving reference frames, as long as one applies the Einstein-Lorentz transformations.

Actual objects are made of elementary particles, atoms with electrons in quantum mechanical orbitals around positively charged nuclei.

Why do solids tend to not want to be able to intersect? In a nutshell, electromagnetism and quantum mechanics. Your plain old atom has electrons which can't get too close to the nucleus, even though they are attracted to the nucleus, because of the uncertainty principle & Pauli exclusion principle. Now you have another atom connected to another solid body coming close and trying to pass through. Now its extra electrons are getting squeezed closer to the nuclei (and other electrons) of the first atom, but the repulsion from the other electrons and quantum mechanics pushes back on it. There is no violation of the uncertainty principle & exclusion principle ever allowed.

Now, go in a co-moving frame of the atom of the heavier body. It can keep stationary while the first body's atom bounces off. In a different frame, this means the train doesn't ever stop even if when it hits the mosquito.

One must resolve these seeming paradoxes not by linguistic reasoning, which is what Greeks and medieval philosophers did, but direct understanding of the laws of Nature underlying our specific Universe.