That sounds very interesting! I'm thinking about the following approach:
I'll help you design a nice excel sheet, which will allow you to enter all employees (ID, name or both) and their start date ect. In parallel, you will have a google calendar, lets call it combined calendar, which displays all vacation days of all employees, for you to have an easy overview any time you need. My program will only ask you for the employee ID, and once provided will provide a new, separate, calendar file for you to open in a calendar, marking all the days the employee can take vacation. It will also provide you the amount of days he has left. That makes easy for you to have an overview and decide on the days. Once decided, you go back to the combined calendar and enter his vacation. We can include a "check calendar" function, to check the new calendar if everything was entered correctly (not too much vacation days ect).
This is just a rough overview with some ideas. We can discuss more once you decide to hire me. I know the price is high but for this project I would like to take my time and do it right. You don't want to end up with a program that makes errors or is just a pain to use. With that budget we can make something nice and trustworthy. The budget includes us going back and forth a couple of times to suit your needs. We can also include some other small features like printing a list of all remaining vacation days for all workers ect.
Looking forward to hearing from you!
Stefa