This year my birthday falls on Mother's Day, which is supposed to be my ex-wife's day with our child.
However, I'd like to see my child on my birthday, but she is unwilling to even split time.
Does my birthday or a holiday take precedent when it comes to which parent gets visitation with our child?
I am unable to give you legal advice on divorce. I can give general divorce help for men, though, my knowledge is based on New York divorce laws where I am licensed to practice.
In general, there is no "rule" as to what day (i.e., Mother's Day or your birthday) takes precedence for visitation purposes. I would suggest referencing any parenting time agreement that you have regarding visitation and attempting to come to an agreement with the child's mother.
While you could certainly file a Petition with the court, my experience is that the courts expect parties to resolve such disagreements among themselves, as doing so typically benefits the child.
Remember, I am unable to provide you with anything more than divorce tips for men, so please consult with divorce lawyers for men in your jurisdiction.