This has nothing to do with dominance. Check the sidebar. Pit bulls just tend to be pretty intense and are prone to dog-aggression (which may not develop 'til later, if at all).

It's scary being a chihuahua. Everything else is huge and intimidating. I would make sure she associates his presence with positive things (treats, play, etc.) but obviously that's difficult if he's being possessive of treats and it makes her uncomfortable when he joins play. Right now what she may need most is reassurance that she is safe. This is where it'll really help to read up on body language. Subtle signals like lip licking (when no food is present), ears back, and raising a paw are signs that a dog is uncomfortable. The moment she seems uncomfortable I would make sure the pit puppy is not allowed to invade her space. Reassure her any way you can. If she wants to retreat somewhere safe, let her. She needs to know she has that option. It's really of tricky to give any specific guidance without seeing their behavior in person, so you may need to tweak techniques. A private trainer coming into your home to observe and pick up on things you may not even be aware of can be a massive help in a case like this. They can develop a training plan based on your individual dogs and situation. But be prepared for the possibility that the chihuahua may only ever be comfortable being an only dog.

As for feeding, I would let them eat separately. In fact with resource guarders we recommend feeding them in a crate as a precaution. When dogs guard food around other dogs it can be tricky to work with (it's easier if they guard from people). This is where it's often just easier to manage it by feeding them separately in crates/rooms so they can't get to each other. With the pit crated for safety, you could also toss a really high-value treat (hot dogs, cheese, etc.) into the food bowl or crate every time he sees the chihuahua. He should eventually make the connection that GOOD things happen when she comes near and there's no risk of his food being taken. But for the most part, management via separate feeding will be your best friend here.

Make sure the classes are based in positive reinforcement. No training collars or leash corrections - those are completely inappropriate for dealing with the issues here. You want training that focuses on counter conditioning the dogs' emotional responses into something positive. Make sure the class is an enjoyable experience for both of them. It can be overwhelming for some dogs.