But the royal family owns a vast amount of land. If they have a badger problem on that land and they would like the government to do something about, how do you think they should do it?

The state owns a vast amount of land, which for historical reasons is used by the sovereign. (Duchies or Cornwall and Lancaster.)

If the Forestry Commission (managing forest land owned by the state) has a problem they write to the government, but their writing is public and they are accountable, ultimately, to the electorate. The royal family should follow the same process, or else return the land to be managed by DEFRA.

Give the land to the government?

It doesn't seem to me as if they got it through legitimate ways to begin with. Royalty never struck me as fair play.

Now that's a knee jerk solution, not an actual one that would work in the real world.

It would work just fine in the real world. It's just that no entity that ever came by such wealth through whatever means would give it up because it was the right thing to do.

Being impartial does not require a lack of opinion. The monarch retains the right to advise the government and express her opinions. Current practice is a weekly meeting with the PM. Once her opinions have been expressed, she must then follow the advice of her government.

I assume this right to express an opinion extends to Prince Charles and the other royals.