I believe using positive reinforcement won’t suppress signals of your dog being in early discomfort. Signs of early discomfort in most dogs are licking lips, stiff body, hair standing on end, looking sideways or staring at the object of concern and ears being pricked. This will often progress to growl, lip curling, body being rigid. If the dog gets more uncomfortable in her situation she may well progress to a lunge or bite or snap.
Negative based training like tugging the lead, saying ‘NO’ and methods that are based on pack theory and alpha dogs can have the potential in some dogs to suppress the early warning signs I’ve listed above. Those dogs will appear temporarily ‘better’ but at some point in the future the aggressive outbursts return only they now appear unpredictable. The early warning signs are suppressed so the dog goes from looking normal to suddenly aggressive.
Training your dog to wear a muzzle is a really good idea. It’s important to keep others safe if our dogs appear unpredictable. A very good behaviourist friend of mine used to say you need to be on your guard 100% of the time in order to make sure the odd aggressive outburst doesn’t slip through your defences and cause harm otherwise you will be forced into a situation where you might need to consider euthanasia.
I believe if you a conflict in the family where your husband thinks euthanasia is a good idea but you don’t understandibly then you really could do with a behaviourist who can look at your situation in detail, look at your dog’s behaviour in detail including viewing her behaviour when out and about and then working with you and your dog on a one to one to improve your situation.
I’m not going to lie it requires a great investment both in terms of time and money to care for a dog with unpredictable outbursts. Your behaviourist will be able to give you more info about whether you can expect to be able to manage the situation better. Ultimately your dog may not change. We won’t know until we try.