I need a battery changed in my watch at a Jewish owned jewelry store that’s open on Shabbos. Can I leave my watch there on friday 5 hours before Shabbos and then pick it up on Sunday? On Friday there’s only one person working there, but on Shabbos there are 2. The person told me that there’s a good chance it will be fixed on Saturday due to personnel, although I left it there in plenty of time on Friday?
If the workers in the store are non-Jews, the fact that the store is of Jewish ownership does not make a difference to you. The owner of the store is transgressing a prohibition by keeping the store open, irrespective of your custom.
Concerning the question itself, if you allow plenty of time before Shabbos for fixing the watch, the fact that the workers in the store choose to do it on Shabbos is not your concern, and it is permitted to leave the watch on Friday and to pick it up on Sunday.
Again, this is permitted because there is sufficient time to do the job on Friday.
See Shulchan Aruch 252:2, 4; Magen Avraham307:3.