I too remember that incident, Mygreendress. It involved Julia Somerville and her partner, Jeremy Dixon (who is now Sir (David) Jeremy Dixon. The child was her daughter from her previous marriage who was about seven or eight. Jeremy Dixon took nearly a whole reel of her standing in the bath with foam sliding off her body. I would have thought that weird too. However, charges were dropped.
The late Queen would certainly not have been enraged by Harry and Meghan calling their daughter, "Lilibet". That is typical tabloid hyperbole. In any case, the girl is bound to be known as, 'Lily/Lili', as she gets older, if not now. It was a nice gesture of the couple to affectionately name their daughter after the Queen. I don't particularly care for the name but that is not relevant, they like it and they live in America where all sorts of names are created.