Dogs will be dogs.

Firstly the barbed wire fencing she goes through on walks, is it just in one particular field? If so I would recall her to be close when in this field, call her well before she gets anywhere near the fence or get her attention by playing a game of ball, dummy retrieve, frisbee whatever you can get her interested in to keep her from going on the scent and passing through the barbed wire, quite simply just distract her. If none of this is possible due to perhaps bad recall, then rather than risk her health I would lead her and run off her energy elsewhere or with ball play.
Re: Hattie getting to the wounds and her ears, the answer is if you are not in the room to supervise and distract Hattie from this behaviour then you need to keep them in seperate areas until her ears and wounds are healed, they may well enjoy each others company but it is more important to have Lottie recovered and not re-infected. You need to keep using the word No! whenever Hattie looks as though she is going to have a good lick and reward her when she listens to you, but keep ontop of not allowing it to happen, on a night time get a dog gate up or keep Lottie with you until she heals. Dogs will automatically lick a wound, you can only distract her from continuing.