If you have excessive appts that interfere with your duty, your command can discuss alternatives such as: having a care provider take them to the doctor, having the parents alternate appts. Now this would be rare and usually a chain of command would only consider this if the appointments were excessive in nature. Keep in mind you can be separated in rare situations if your parental duties interfere with your duties. See AR 600-20 with regard to family care plans, and AR 635-200 with regard to separations.
Usually these issues can be resolved by speaking with members of the chain of command. If necessary consider speaking with both your 1SG/Commander on open door policy together.