What is the ruling of Islamic law regarding the wife's brother opening a shop adjacent to my relative's shop, selling the same products that my relative sells?

It is not forbidden for your son-in-law to open a shop next to yours with the same commercial activity, nor does this fall under the category of "one brother selling over another's sale," even if he used to work with you previously. It would have been better for him to choose another location to avoid potential competition, but sustenance is predetermined, and no soul will die until it has received its full sustenance.