When to withdraw/is this professor being reasonable?
In the US, it is up to the professor on how he/she wants to handle a student missing class without a valid excuse. Vacations are not valid excuses (doesn't matter how long you've been planning it, and why would it?).

However, medical issues are a valid excuse and the university usually has a policy on how to handle it, which professors have to adhere to. I would recommend talking to your advisor or the chair of the department about this. 

As @ChrisPhan mentioned, this particular situations looks to be protected by Title IX in the US. Most universities have staff known as Title IX Coordinators that you can contact. I imagine that they will take this very seriously.