The answer to your
say I took a slow moving atom and hit it with a baseball bat to give it some extra kinetic energy.
This is not possible within what we know in mainstream physics.
Atoms are ruled by the laws of quantum mechanics, as was found during the last century, which are not the same as the rules of classical mechanics of the bat. In addition a bat has about $10^{23}$ atoms per mole of mass, and one cannot model quantum mechanically the impact on one atom.
As far as I understand it this kinetic energy is mostly within the heavy nucleus.
Suppose you scatter an atom off another atom, kinetic energy can be exchanged while the total energy is conserved, but the motion will be with the whole atom, not just the nucleus.
How does this kinetic energy of the atom then manifest into an electronic excitation like if we heat up the atom it will emit radiation?
If an atom interacts/scatters with another atom, due to the kinetic energy of the temperature in a material, the electric fields can interact, and energy can be transferred to an electron to eject it and ionize the atom. Quantum mechanical interactions .