We simulate a tug-of-war (TOW) scenario for a model double-stranded DNA threading through a double nanopore (DNP) system. The DNA, simultaneously captured at both pores, is subject to two equal and opposite forces -f[over ⃗]_{L}=f[over ⃗]_{R} (TOW), where f[over ⃗]_{L} and f[over ⃗]_{R} are the forces applied to the left and the right pore, respectively. Even though the net force on the DNA polymer Δf[over ⃗]_{LR}=f[over ⃗]_{L}+f[over ⃗]_{R}=0, the mean first passage time (MFPT) 〈τ〉 depends on the magnitude of the TOW forces |f_{L}|=|f_{R}|=f_{LR}. We qualitatively explain this dependence of 〈τ〉 on f_{LR} from the known results for the single-pore translocation of a triblock copolymer A-B-A with ℓ_{pB}>ℓ_{pA}, where ℓ_{pA} and ℓ_{pB} are the persistence length of the A and B segments, respectively. We demonstrate that the time of flight of a monomer with index m [〈τ_{LR}(m)〉] from one pore to the other exhibits quasiperiodic structure commensurate with the distance between the pores d_{LR}. Finally, we study the situation where we offset the TOW biases so that Δf[over ⃗]_{LR}=f[over ⃗]_{L}+f[over ⃗]_{R}≠0, and qualitatively reproduce the experimental result of the dependence of the MFPT on Δf[over ⃗]_{LR}. We demonstrate that, for a moderate bias, the MFPT for the DNP system for a chain length N follows the same scaling ansatz as that for the single nanopore, 〈τ〉=(AN^{1+ν}+η_{pore}N)(Δf_{LR})^{-1}, where η_{pore} is the pore friction, which enables us to estimate 〈τ〉 for a long chain. Our Brownian dynamics simulation studies provide fundamental insights and valuable information about the details of the translocation speed obtained from 〈τ_{LR}(m)〉, and accuracy of the translation of the data obtained in the time domain to units of genomic distances.