My fiancés dog, Tsosie is food aggressive and attacks my dog, Ozzy.

My fiancés dog Tsosie (Australian Shepherd/ Border Collie mix?) is extremely aggressive and territorial when food is around.
Tsosie (she) will attack Ozzy (griffon mix) and go for the ears and throat. She has already drawn blood multiple times.

For the most part they get a long very well when food is not around, but there have also been a couple occasions when she will attack him unprovoked, and or if she gets excited during walks and sees or hears another barking or excited dog across the street or nearby.

The first incident occurred when first I moved in. I was holding a bag of Ozzy’s food and when I put the bag down, she attacked Ozzy. This happened about 6months after they were introduced on a walk and play date at a local park. We were all caught off guard.

Tsosie is a “Res” or Reservation dog. She was found when she was a puppy about 5years ago by my fiancé and her daughter.
I made the observation that she is more than likely food aggressive because it is in her nature to be so considering that’s how “wild dogs” have to be to survive.

We have taken measure and place Tsosie in a cage when any food is around and at their meal times.

But my major concern is the unpredictable nature of her aggressive behavior.
On one occasion we were getting ready to go on a walk and out of nowhere she snapped and bit his ear causing a laceration.

Outside of what I have explained, Tsosie is very gentle with adults and kids. She is very cuddly and sweet with me, my fiancé and her daughter.
And she shows affection and plays with Ozzy all the time. They’re best pals.

My fiancé has had enough of her behavior and wants to rehome her. What do you all think?
Any recommendations?
Over the past year, I have trained her with the gentle lead during walks, recall, and commands.
It just seems that her aggression might be too primal.