If my wife has a doctor's appointment and I need to take her to it, do I have to take a chargeable leave day?

Leave or pass, those are the only two "official" and legitimate ways to be absent from your place of duty.

That said, Using the hands and feet of every senior NCO on this forum I doubt I could count the number of times I gave "permission" for a SM to go to a family member appointment during duty hours. The only time I made it official as in pass, was if they had to leave the local area, and the only time I had to make them take leave was if it would going to take more then a normal duty day or leaving the "Norm" area in milage for a pass

The dilemma here is how is the office covered while you are gone?

From what you described I don't see much of a problem.

One of the very view direct orders I ever gave was to tell an airman to take the day off. He kept working at busy work until I told him if he didn't leave he and I were spend all weekend at work.

It Seems in one form or another if Your scheduled for duty and You can't arrange something on Your own time then You need to be excused from duty. I don't feel You should have to take leave for that but You do need approval if its not on Your own time esp if in a situation someone else has to pick up Your duties while You are at Her Appointment.

Recommend you call the office you work with or for, tell the person you talk to regularly what you're going to do and the hours you will be gone and ensure they have your cell number. Leave a message on the office phone that you are out of the office and will return at (time). If you have drop in visitors, leave a note on the door with your intended return time and your cell number as an emergency contact number.

Take your wife...never heard of an NCO having a problem with this.

Find the regulation that defines the length of a duty day? It doesn't exist to my knowledge and the duty day is mission and supervisor dependent.
It sounds like that same supervisor is no longer willing to be flexible with you in which case yes they could force you to take leave or pass to cover your absence. Something made them suddenly aware or concerned about your time out of office. Maybe you abused the privilege and it has caught up to you or maybe they had a bad day. It is well within their purview, but have a better conversation with them if possible as maybe they can explain more of why they are acting this way.

Is there anyone in the Unit that is close by for they could watch and help someone if they needed too so could take her?
SSG MARK FRANZEN
USA VET

check and see what the State has in the benefits package on family support

I had to take a lot of phone calls, etc. for reserve stuff during working hours at the regular job. The bosses knew I just added time to my day to offset it and life was good. Bottom line, if you're not working, make sure you make it up and give the taxpayer their worth. It's usually recognized as a good attribute of an honest and valued employee.

If your commander doesn't mind then you should be okay.