Question

justification for increase in entropy during mixing of ideal gases is the driving force for mixing​

Answer 1

For ideal gases, the entropy of mixing at prescribed common temperature and pressure has nothing to do with mixing in the sense of intermingling and interactions of molecular species, but is only to do with expansion into the common volume.

For an ideal gas, the energy is not a function of volume, and, for each gas, there is no change in temperature. (The energy of the overall system is unchanged, the two gases were at the same temperature initially, so the final temperature is the same as the initial temperature.) The entropy change of each gas is thus the same as that for a reversible isothermal expansion from the initial specific volume to the final specific volume.