Consult your local orthodox rabbi. Not all agree that a restaurant being open on shabbos necessarily renders the food unkosher or kashrus unreliable in general. (I know that may come as a shock to some people, but I had a shaila (question) like this and a place was permitted to me to eat there during the week despite being open on shabbos when I asked my rav, and they had a reliable kosher certification). A person should find out what certificarion the place has, then present these facts to their rabbi and ask for a psak din whether they can eat there.