Delta is giving my wife crap every time she checks in with PSD

My wife has flown 3 times in the last 2 months and 2 of those times from our home base the check-in attendant has taken over 10 minutes to process her service dog.

Each time we have had to email the DOT form to their specific email and they claim that we will get a code back that they enter into her account so we don't have to go through this process each time. Yet, we have never received a response; resulting in us having this issue each time.

This most recent time, the lady asked her question about what services the service animal provides to the owner. My wife, having generalized anxiety and panic disorder (this being the reason she has a PSD), froze in the moment and said 'I get really bad anxiety and sometimes get panic attacks and I use his body and warmth to help calm me.'

This is technically correct, although does not sound as official as it could have been. But I feel I cannot be answering for her as we are both adults and I don't want to look like I am controlling my wife in front of the Delta employee. Even though my wife would prefer I answer for her because of her anxiety.

Long story short, the employee then begins to hassle my wife and claims that her response means that her dog is an ESA, not a service dog so it doesn't count. This leads to my wife almost freaking out so I stepped in and said "Her dog is a psychiatric service dog that provides tactile stimulation to her when he senses that her anxiety is rising, in an attempt to prevent a panic attack."

She did not seem to enjoy my response and scoffed at us and said, "I will let you go through this time but I am making a note on your account for review of this service animal because this should not be allowed."

I am not sure what to do from here because I trained this animal (to my best estimate, close to 300 hours over the last 9 months or so) to provide these specific services to my wife and she is usually flying alone (I used to be there for her to help calm her and could notice if things were triggering and had methods of taking her attention away from those).

I am worried about what will happen when she is on her return flight home in 7 days when I am not there to help her present this information to the representative (assuming they are the same way as this experience).