You're right; you shouldn't have to count that as a day off because you are open. It's not like you're taking off a couple hours to go drinking with your girlfriends--you have the once a month appointments for your condition (which you can't help, I assume
) and now something else came up--the dental work. Perfectly reasonable to me!
If the parents feel like you needing to take care of your body and your health is not acceptable, then you are probably better off with someone else anyway.
Can you schedule the dental appointments for the same days as your other appointments, at back-to-back times, so you need more like a half-day replacement once a month?