Perhaps the TM is confusing driving time and duty time. You could be proactive and go for a short run with her (lets say 15 mins) and its fairly easy to show that driving time and duty time differ - do a load of stop start with +30 secs stopped and it will show the difference. Isn’t or wasn’t this the whole point a while back of the tacos being set to show rest if driving for less than a minute (less than 31 secs as its the nearest minute)
Is there a reason for the fixation on your travel times? Perhaps to make it easier for the TM mot extract the info they want, then they could fit a cheap and cheerful telematics, logger or tracker. It would at least avoid the conflict between the times you can give and the times the TM wants.
Ask what her concerns are about moving vehicles in the yard. It does sound rather nonsensical It is possible that she is concerned about missing mileage, but if you are in small yard that is hardly likely to happen.
The main challenge that is happening at your site is the age old one of “communication”. It sounds like the TM is not communicating how and hwy they want these things done.