Is it permissible to work in a hotel where alcohol is sold, provided one is limited to serving only permissible foods and beverages, and to record the number of alcoholic drinks in inventory without touching or selling them?

It is not permissible for you to work in this place that serves alcoholic beverages, due to the involvement with sinful acts, even if you do not directly serve the alcohol. You must leave this job unless you are compelled to stay, in which case you remain only to the extent of the necessity, and you should search for another job, even if its salary is lower. Necessity means that a person would not find food, clothing, or shelter for himself and his dependents if he were to leave this job.