What is the force carrier for neutrons in fission? Say I have a neutron capture event, leading to a fission reaction in which a few neutrons are expelled. These neutrons inherit a certain momentum from this fission reaction.
How do these neutrons obtain that momentum? Is there some kind of electromagnetic interaction between the nucleus and the neutron’s dipole moment? Or are there different interactions at play here?
 A: The short answer is that the force carriers are mostly pions, but the details get quite complicated.
In physics we know about four fundamental interactions: the strong force, the electromagnetic force, the weak force, and gravitation.  The neutron participates in all of them, but feebly.  Its gravitational mass is small, it has no electric charge, and its magnetic moment is smaller than the magnetic moment of the electron by approximately the ratio of the electron and neutron masses --- that kills the long-range $1/r^2$ forces.  The strong and weak forces are both contact interactions with finite range, but the strong force is ... stronger.  So when a neutron is near enough to a nucleus to undergo scattering, including only the strong interaction is usually a pretty good approximation.
Microscopically, the strong interaction is an interaction between color charges, mediated by gluons.  However at the low energies involved in nuclear fission, quarks and gluons are not the degrees of freedom which give the most parsimonious explanations of what's happening in QCD.  Instead, the QCD vacuum condenses into color singlet states like the proton and neutron, which interact by exchanging color-singlet mesons like the pion, the rho, the omega, and others.  These mesons effectively give the nucleons a set of Yukawa interaction potentials which are exponential in the meson masses, so the lightest meson (the pion) contributes the most to the interaction except at very short distances.
