On a personal level, my boss knows my DD is more important than my boss and the company I work for, especially on her birthday. Is your boss or their company really more important to you than your child/ren on their birthday of all days?

That's funny.
Of course my dc are the most important thing in the world to me, but that doesn't mean the rest of the World stops for them.
Are you saying your children are an inconvenience to you if you have to miss one day of your hobby for such an important day to them?
No, I've not said that anywhere. Not sure why you are making things up.
However, no-one in our family expect the world to stop for them. We all make arrangements when it is most convenient for the most people (of the people you want there).
One of the first days I book annual leave for every year is my DD birthday so I can spend it with her
I don't know if your dc are school age? If so, you must be in a pretty unusual job to have enough AL to cover the school holiday, any sickness they have, Training days and add birthdays on to that. Do you still book the day off when they are in school all day ? 
I want her to know that she is important to me and I want to spend her special day with her.
Trust me, my dc know they are my world. They also know that I have responsibilities to work, and in my volunteering, but that we will ALWAYS spend time together to celebrate their birthdays (and mine), and, when they were younger, also again, separately, with their schoolfriends.
However on a separate note you can’t put work and a hobby in the same box of equal importance
Well, some people do have responsibilities and commitments in their volunteering and hobby roles, which doesn't seem to have occurred to you.