Convert video with ffmpeg to have the same quality
The differences between your "works" and "doesn't work" examples are:


resolution
framerate
Codec Tag
Codec Level


and you can set these using ffmpeg:

ffmpeg.exe -i /temp/input.mp4 -c:v mpeg4 -level 3.0 -vtag XVID -s 544x416 -r 25 -qscale 0 /temp/out.avi


Qscale 0 will produce a large file but maintain the best quality. 

Please note that changing the resolution and frame rate will not produce the best output quality, so check if you can just omit the -s and -r parameters to maintain the best quality. Possibly you need to set the bitrate to 800kBit as in your "works" example to make it work on the target device of your grandmother.