Yes the RAF should fly the Royal Family around when on official duties, they should charter only when on private trips.
Not in the forces, nor a pilot, nor particularly a royalist, but for goodness sake some of the Royal Family are damn good value for money bringing in far more in tourism etc than we pay out.
We are not a republic and I don't ever want to be part of one, as was said earlier the R stands for Royal.
As far as the EU treaty is concerned I think you will find that our constitution does give the Queen the right to refuse to sign the Royal Assent document, at which point it goes back to Parliament.