Many scientist believe that there are even smaller particles called quarks, these quarks make up an atom. They also think that there are gluons, small particles that "glue" these quarks together. The gluon "glues" the nuetron together with a force, known as the strong force. They think that in a nuetron, there is some residual strong force that "glues" the protons together. See, like charges repell, so the positive forces of the proton should repell each other, but the strong force is strong enough to overcome that electrostatic repullsion. I, simply, learned this from research, I have no idea how they theorized this or what type of research was done to devolope this theory.
Now, the scientists think that the nuetron and proton are composed of three quarks, there are up-quarks and down-quarks.
Up-quark has a charge of +2/3.
down-quark has a charge of -1/3.
Neutron has an up-quark and a down-quark.
2/3 - 1/3 - 1/3 = 0
Proton has a down-quark and two up-quarks.
2/3 + 2/3 - 1/3 = 1
As for stripping off the electrons, that would just ionize the atom.