Molecular dynamics (MD) simulations using many-body polarizable force field were performed on comb-branched poly(epoxide ether) (PEPE) polymer electrolytes doped with lithium bistrifluoromethanesulfonamide (LiTFSI) salt as a function of temperatures from 333 to 423 K at ether oxygen (EO) to lithium ratio of 20. MD simulations predicted electrolyte conductivity in good agreement with experiments. The fraction of solvent-separated ions and lithium cation environment for PEPE/LiTFSI were similar to those found for the linear poly(ethylene oxide) (PEO)/LiTFSI electrolyte. The Li+ cations had the highest probability to be coordinated by EOs near the PEPE polymer backbone and the lowest probability being coordinated by EO's at the end of side chains. Segmental dynamics of the backbone was slower by 2 orders of magnitude compared to the dynamics of side-chain ends. The Li+ self-diffusion coefficient was approximately an order of magnitude lower than the TFSI- anion self-diffusion coefficient. Visualization of the lithium motion revealed that the most mobile Li+ cations moved by hopping from a side chain to another without being complexed by the backbone. The influence of the backbone-Li+ interactions and the backbone stiffness on ion transport was investigated in MD simulations performed on the PEPE/LiTFSI-like electrolytes with the same PEPE architecture but a very stiff backbone that does not complex lithium cations. The ion transport in these model electrolytes was compared to that of the original PEPE/LiTFSI electrolyte.