Scoobydoobywho
I feel your pain. I am in a similar situation. I have answered that you ARE being unreasonable if it is a one off and not for long at all. And that they are willing to move as soon as they are asked with no abuse or argument.
You are definitely NOT being unreasonable if this is a regular occurrence and this is a regular Cheeky Parker who thinks this is their personal waiting space.
In my own borough, I have had it clarified that in fact, the only people who have the authority to park over my drive is a residence of my home before it had double yellow lines. It is only with authority from a resident, that anyone can park there across the driveway. So those stating you do not 'own' the road, actually, you kind of do in a way that you can park there or authorise someone who parks there.
I now have double yellows, so I do not know quite if I can even do that now. I don't think I can.
People cannot wait on double yellows either.
Time to talk to your school again. In my case, people waiting or parking over my drive reduces dramatically the visibility of the children crossing the road to enter the school gate (there is no formal crossing place able to be placed on this road) . The school has in the past asked for a photo of the car and they send it out in a newsletter with a request for the illegal parking and waiting to stop.
HTH