Regarding driving hours, the simple solution would be a form where you put “from”, “to”, “departure” and “arrival” time on each line for each leg of the journey.
Then she can see you went off from X and got to Y at certain times. Maybe include an “issues” column too for things like diversions, road closures etc. Then she can see how long it takes etc. Keeps her happy and she might stop complaining about driving times.
As for moving trucks - loads do it in various ysrds without a licence. Having to do checks before moving may be a bit OTT but if its company policy nothing you can do. Just keep out the way.
On brake lights, if its a DAF see if theres a 3rd button on remote. Press amd hold for 2 seconds amd it runs though lights (not sure if its on rigids). If no one on the yard and its dark, you can see them anyway.
Would agree, if paid hourly just go with flow and let them see the costs go up. Keeping a timesheet will defo help you esp if you addon “vehicle checks” etc. to show bosses how long things take.