We use molecular dynamics (MD) simulations to understand the structure, and stability of various Paranemic crossover (PX) DNA molecules and their topoisomer JX molecules, synthesized recently by Seeman and coworkers at New York University (NYU). Our studies include all atoms (4432 to 6215) of the PX structures with an explicit description of solvent and ions (for a total of up to 42,000 atoms) with periodic boundary conditions. We report the effect of divalent counterions Mg(+2) on the structural and thermodynamic properties of these molecules and compare them to our previously reported results in presence of monovalent Na+ ions. The dynamic structures averaged over the 3-nanosecond simulations preserves the Watson-Crick hydrogen bonding as well as the helical structure. We find that PX65 is the most stable structure both in Na+ and Mg(+2) in accordance with the experimental results. PX65 has helical twist and other helical structural parameters close to the values for normal B-DNA of similar length and sequence. Our strain energy calculations demonstrate that stability of the crossover structure increases with the increase in crossover points.