If your player can handle it just make it perform the side-by-side view. No encoding or muxing required.
mpv video player
Example using mpv:
mpv --lavfi-complex="[vid1][vid2]hstack[vo];[aid1][aid2]amix[ao]" input1.mp4 --external-file=input2.mp4
The above example assumes each input has the same height. Otherwise you will have to add the scale, scale2ref, pad, and/or crop filters. Simple example using the crop filter to remove 20 pixels from the height:
mpv --lavfi-complex="[vid1]crop=iw:ih-20[c];[c][vid2]hstack[vo];[aid1][aid2]amix[ao]" input1.mp4 --external-file=input2.mp4
See the mpv documentation and FFmpeg Filters for more info.
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