To my knowledge there is no regulation governing Soldier appointments. The leader has a responsibility to manage his Soldiers’ time away from work so that it does not unfairly impact the mission or esprit de corps of the unit. You typically cannot refuse a Soldier the right to appear in court if they have been ordered to appear in court. There are some exceptions. As far as OB/GYM: the command can refuse to allow a Soldier to go to an appointment that interferes with the mission. If the appointment deals with the direct health of the Soldier, then the Soldier should be allowed to go to the appointment. The command can direct that normal appointments must be cleared through them within a reasonable time frame (24-72 hours prior, for example).
If the command believes the Soldier is not capable of performing as a Soldier because of family issues requiring too many appointments, the command could implement a family care plan requirement under the provisions of AR 600-20. If the Soldier is unable to develop a care plan or fails to implement it in a manner that allows them to complete their duties, they can be separated from service.
Most commands will allow reasonable requests for appointments. It is only when it begins to effect the mission or the appointments appear to be excessive and the Soldier’s performance is in question that most commands will begin to crack down.