Since you don't really know how the dog was raised, treated, or possibly traumatized, this is going to take time. Since she was underweight, it is safe to assume she was starved. It is only logical that if she has been undernourished, she will do anything to get and keep her food.
The first thing I would want to do is make sure it is just food aggression. By this time, it seems you have introduced the dogs. I would not have recommended doing so on leash -- that makes the dog feel constrained and unable to use flight instinct, and more likely to use fight instinct if she feels threatened. But apparently that didn't happen, so good -- probably not leash aggressive.
How about territorial? If she is laying in an area and another dog approaches, does she do anything aggressive to let the other dog know not to come into her space?
How about toys? Is she possessive and aggressive with toys?
Any other circumstances where you have spotted aggressive behavior other than food?
What was happening in the kitchen? Were they eating? Was their food being prepared? Was human food being prepared? Exactly what were the circumstances before the incident?
What are the sexes of all the dogs, and are they all neutered/spayed?
If they were feeding, and another dog tried to take food from her bowl, well, that is actually rude, and it is dominant behavior. Her response was (to us) inappropriate, but then again these dogs are wild animals so in that sense her response was probably somewhat natural.
If you have not seen any other signs of aggression, except with food, I would say work on it. But if you have seen other signs, like territorial aggression, aggression over toys, aggression when the other dogs "sniff her out", etc. then it might be best if the dog is rehomed to a home without dogs and also without children -- kids will walk up to a dog and steal toys, and even walk up and put their hand in their food bowl. That would be disastrous
I would say that in all honesty, the situation probably is not good. Being protective of food and using aggression is somewhat normal behavior for a wild animal. So is eliminating in the house. These two things may not seem to be closely related, but they really are by virtue of being natural behaviors. We all go through the house training process, and most are able to complete that training to a very high degree and can count on their dogs not eliminating in the house. But the chance is always there that the dog might regress, but the worst case is that you have to clean up a mess.
On the other hand, you can try to train the rescue dog not to be aggressive over food, and with time and patience you can do so. However, there is also always that possibility that the dog will regress, and the result could be very disasterous.
Eliminating behavior is one thing, but this really gets to the core of the dog's temperament, and I doubt you will ever be able to completely trust a dog with an aggressive temperament.
Your best case scenario is to learn to manage it, and understand that managing it is probably all you can do and carries risk.
A behaviorist that works with your dog on this issue also assumes risk, because if your dog ever reverts and injures a dog, or worse a person, then the behaviorist may have some liability
