] Wasn't it frowned upon, though, to have women aboard a ship? Or was this normal in His Majesty's Navy at the time?

Not only was it normal for officers' wives to accompany their husbands (Mrs Croft talks about how much time she has spent at sea), women actually fought in ships. Many women fought at the battle of Trafalgar, helping to load guns, nursing the wounded etc, and they were refused medals after the event.

There's information in the archives if you are interested.