Moving one-dimensional electromagnetic solitons formed in a weakly relativistic laser-plasma are studied in the generalized nonlinear Schroedinger equation model. Conserved quantities and moving soliton solutions are analytically derived in a closed form. Stability studies reveal a transition at maximum amplitude to an unstable cusp-soliton. Simulations of two interacting electromagnetic (EM) solitons show a critical dependence on the solitons' amplitude, velocity and mutual phase; resulting in either elastic collisions or a break up of the soliton pair.