The title of this question refers to the emission of light from an incandescent light bulb, and then the body of the question asks for Planck-scale details of the physics happening there. Well, that would be a lot of work to answer.
Suppose it's a tungsten filament. Then there's a molecular lattice of tungsten atoms, i.e. a lattice of nuclei surrounded by electron shells embedded in a "Fermi liquid" of conducting electrons. The nuclei are spinning balls of protons and neutrons exchanging pions; the protons, neutrons and pions are all made of quarks and gluons. The electrons in the shells are electromagnetically attracted to the protons in the nuclei. The conducting electrons are also attracted, but their wavefunctions are spread out in space, throughout the tungsten wire.
As John Rennie's comment points out, the emission of photons from an incandescent light bulb comes from these spread-out conducting electrons, not from the localized electrons in the electron shells. Emission of photons from electrons associated with a single atom, is more characteristic of a gas, where the atoms are floating free.
But there is a sub-question about how the quarks in the nucleus respond to the electron emitting a photon, and that's easier to answer in the case of a free atom. Basically, there is no effect, but I should be able to explain why.
The effect on an atom, when one of its electrons emits a photon, might be vaguely like what would happen, if you had a balloon with some marbles inside it, and then you tapped on the balloon. The balloon would move away, but it would wobble and the marbles would rattle against each other. Here the balloon is the wavefunction of the electron which emits the photon, the tap on the balloon is the impulse that the electron experiences in the opposite direction to the photon, and the marbles are the wavefunctions of the quarks, or even of the protons and neutrons.
I think the main thing to understand is that when the photon is emitted, conservation of momentum means that the electron, and then the whole atom, will start moving in the opposite direction, but very very slowly. If you think of the balloon again, and suppose it was floating there but with a fly resting on it, and then the fly took off. The balloon would start moving away in the opposite direction to the fly, but very very slowly. The whole atom would move back from the emission of the photon, but only slowly, and the effect in the nucleus is indirect, like the rattling of the marbles in the balloon.
So the recoil on the atom is almost zero, and it will be completely drowned out if there are other forces acting on the atom, e.g. if the atom is bonded to other atoms and the whole structure is vibrating with heat.
Returning to the general topic of the subatomic physics of incandescence, or the subatomic physics of anything, the main challenge for any questioner is going to be, understanding what wavefunctions are. It's a wave, that can be spread out in space, or concentrated around one point, which gives the probability for the particle being there. If the "wave" is high in some region, then the probability is high that the particle is in there; but there is also a probability that it is somewhere out in the much larger region where the wave is low.
The way these waves behave has a lot in common with the older ideas of particles experiencing forces, e.g. the old idea of an electron orbiting the nucleus like a planet orbiting a star. The waves in the electron's wavefunction do travel from place to place; but they can also be in an equilibrium configuration, just pulsing on the spot; the energy levels for electrons in an atom are like this.
The big question is, what is actually there? Are the waves real; or is the reality a particle moving around, and the math of waves is just because we don't know where it is; or maybe the reality is some third option? I'm sorry to say that you won't get very sensible answers to this question from physicists. You will get different answers from different physicists, including excuses for not having a proper answer.
This picture of probability waves for particles is about as far as physics has progressed. It provides enough logic and visualization, that many many things can be understood, and predicted with amazing detail. For example, it's a framework capable of describing and explaining incandescent light sources, in terms of what the atoms are doing. But if you want something deeper and more logical than probability waves, you'll just have to wait for the next big leap in physics.