We prove existence and uniqueness for solution of second order BSDEs with jumps (2BS-DEJs). More precisely, our problem of interest consists in the optimization, over a set of possibly non-dominated probability measures, of solutions of backward stochastic differential equations with jumps (BSDEJs). After proving a dynamic programming principle for this control problem in an abstract setting, we obtain a wellposedness result for second order BSDEJs (as introduced in Kazi-Tani, Possamaï, and Zhou [10]) which does not require any regularity assumption on the terminal condition and the generator.