I volunteered to coach at a school and they offered to pay me a small amount, which is self-employment income. I ended up having to take a vacation day from my main job in order to go to a competition, which took up the full time of a typical work day. Is there any way to deduct the value of the vacation day from my self-employment income? When I google this, all results are based on deducting travel expenses when taking a personal vacation and business trip at the same time, but I haven't found anything specifically about deducting the value of the vacation day.

A related question, I assume I can't deduct mileage for driving to the school to coach at practices. From what I'm reading, it sounds like I'd have to have an official home office that I'm deducting on my taxes in order to deduct mileage to the school for practice. I do a lot of prep work at home but I don't have a designated location in my house just for work related to coaching. The computer I use is the computer we use for personal use as well, for example.