Dominance challenges can be anything from a look to a full on physical altercation. It all depends on the type and level of dominance of the dogs involved and whether or not those dogs are balanced.
Ellie is a balanced high level Alpha female and she was very patient and tolerant with Charlotte. An unbalanced Alpha would have planted Charlotte on the ground the second she bunted them. It wasn't until Lotus, the most dominant Alpha female here, gave a second, very assertive bark did Charlotte finally stop challenging Ellie and layed down and relaxed.
In order to understand dog psychology and dog behaviour, you must first understand dominance in the Dog world and how, when and why dominance is projected.
Anyone who claims dominance doesn't exist in dogs does not know or understand dogs. All reactive and aggressive dogs are dominant dogs and therefore the first question you should ask a dog trainer or behaviourist you are thinking of hiring to help you is, "Does dominance exist in dogs?" If they say no then they can not help you with your dominant reactive or aggressive dog.
Cheers ✌️