Disposal operation forces drain water into second sink
And the main stack and vent are located about 4ft to left of double sink.


It seems you needed your vent to be to the right of the sinks. Although the installation is apparently within code for the length of a single trap arm, when the disposal forces water into the drain it is backfeeding the small sink trap. Having the vent to the right would allow air pressure to equalize in that direction instead of through the small sink.

A simpler solution might be a backwater valve for the small sink. Although it may be difficult to find room for it but then you were thinking about moving the disposal so maybe there is room.

Good luck!