First off we need to understand what dominance is about with dogs. It's not about "leadership" it's about who gets what. Dominance is often shown when resources are limited (space, food, etc...) so yeah if you have toys in the mix...bad idea. You're instigating a territorial battle. Take the toys away for a while, or give them each a toy separately to play with (a kong with filled with food) and remove them once done.
Furthermore it's important to understand dog "pack" behavior before introducing another dog into the mix.
Dogs work a little differently than wolves and do not have a typical Alpha pack leader. There are essentially three types of pack mentality for dogs.
Despotic is usually when a dog is so dominant he barely has to do anything to keep others in line. A simple growl and others back off.
Linear is when there's a sort of pecking order but not necessarily a leader. If there was a leader like in a wolf pack the "alpha" dog would hunt for everyone else. Dogs on the other hand are extremely selfish animals concerned with how they can get what they want. This is how we condition them through classical conditioning – because their weakness if often self indulgence like food or toys.
Triangular is very unstable. It's when no dog submits. It doesn't necessarily sound like you have a triangular situation, but you simply might have two dogs, prone to aggression when resources are limited. So when one dog says, "hey this is my toy" and the other dog doesn't pick up on the warning signs, or doesn't care, a fight is going to happen.
What to do?
Do not let them work it out – not when resources are limited. You need to teach your dogs how to behave properly in the house. Clearly they cannot handle the toys yet so remove them from the situation. Do not let them get to frenzy mode. When you see the warning signs (they stop, stare, body goes rigid, etc...) snap them out of it in a humane way.
Note: I have two dogs – one dominant and one with a predisposition to fear aggression – and had to overcome food and toy issues. I also study dog training and work at a doggy day care.