Dominance is a hefty word. I recommend one use it with caution. Can you describe the specific behaviors that are causing you concern? That would give us more insight and allow us to make more specific suggestions

In the meantime, do you use a set of rules, i.e. NILIF? If not, I would implement that now.

Also, I would not worry too much about your Pug teaching your Springer puppy bad habits. Dogs, like every living being, is born with an inherent temperament, or emotional excitability. Thus, temperament is relatively stable. If the dog is naturally mellow and calm as a puppy and it is obviously inherent, then chances are high that he will be a relatively calmer adult.