There is a big difference in a private car park and private land, a private car park is often still a public place. You dont need a license, insurance, mot etc to ride/drive on private land (with permission). Im assuming as it was you on the bike and you showed them your license that you have to produce your insurance? If the car park was a public place, asking you to produce your insurance is fair enough as you could hit another vehicle / person etc.
Also wondering, if you were there teaching your `lass` how to use the gears, Im guessing she hasnt done her CBT, therefore, are you sure the bike has insurance??