While dogs can settle minor disputes with each other (such as growling the other off of a toy or their own food bowl), they shouldn't be limiting each other’s access to you, your family or common areas of the home. In multi-dog households, there isn't usually a dominant dog or submissive dog. Instead, dogs' roles change depending on the context involved. For example, a dog that claims access to a favorite toy may let the other dog claim the couch. Reward polite behavior and manage the environment to prevent conflicts from developing.
For more information, see the booklet “Feeling Outnumbered? How to Manage and Enjoy Your Multi-Dog Household” by Karen London, Ph.D. and Patricia McConnell, Ph.D.