Food Agression?

Please give me advice.

Hello, we are a family of four two older kids and no other pets but our adorable pit/greyhound rescue. He is with us since he was 10 weeks old, he is one year old now. He was very skinny so I began a diet based on dog’s food and brown rice and turkey and vegetables or chicken liver and gizzards . He looks great now and get daily exercise and discipline and rules, he shows a little nervousness about loud noises. But other than that acts healthy and happy, my mother was home with us and her chihuahua which is no strange to our dog, it was feeding time and he doesn’t care as much for his hard food so I though we would feed them the rice mix, I put the chihuahua in a play pan but my dog rushed there to eat it and the chihuahua snapped at him and he barked at her and picked her up and threw her away making some cuts on her snout. I see that it was a mistake to do that, but I’am so concerned that he reacted that way. Please advice on either changing to just hard food that wouldn’t cause agression toward other dogs or what to do? Could this be a sign of a bad problem in the future. What does it mean when a big dog bites a small dog? Thank you in advance for your help
Liz Almon