Family loyal dog for long-term travel

There are several aspects you need to consider, including:

Breed

Traditional herding and guard breeds were bred exactly for your purpose: to protect familiar individuals (animals or humans) from potentially dangerous individuals (animals or humans). Different sites offer different lists and classifications of breeds, like the American Kennel Club.

A mixed breed is no worse or less worthy than a pure breed and often has less medical problems.

I'd stay away from "beautiful" overbred dogs like German Shepherds and Boxers. During the last decades, when the breed lost it's original purpose because keeping sheep wasn't profitable anymore and electric fences where cheaper than dogs, the focus of breeders switched from a functional work dog to a "beautiful" fashion dog. This led to numerous medical problems for the poor animals. If you choose a puppy of one of those breeds, look for "old fashion" and archaic body features in their parents.

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Personality

The breed of a dog has great influence but doesn't define the personality of a dog.

Please have a look at this answer which summarizes the Meet your Match dog assessment system. You'll probably want a socially or internally motivated dog with medium energy level (first or second row, orange category). If you follow the link to the system description, you can find a manual how to assess the character of puppies and adult dogs.

Since your dog needs to be socialized very well, I would only consider shelter dogs that have led a similar life before (meeting strangers on a regular basis) and are not aggressive towards people and other dogs.

Size

A big dog may look intimidating, but it doesn't have to be a giant. An agressively barking Akita is surely more intimidating than a docile Great Dane.

Please consider the available space in your trailer. Will the dog be able to move freely? Will it have enough space to stay inside a whole day when it rains?

And will you be able to hold the leash steady if your dog pulls you full power?

Regulations

There might be some regulations regarding breeds (like fighting dog breeds), taxes and letting dogs run free in an unfenced area. You might not be allowed to bring your dog everywhere, or places might require the dog to be leashed and muzzled at all times.