Can you bring dogs into the park?

Ditto on the cars and no trails

Yes

Dogs are only allowed where your car can go. Service animals are allowed in all areas of all the National Park system.

While dogs are welcome anywhere cars can go (in park campgrounds, in picnic areas and along the shoulders of roads) they are not permitted on any trails. They must be on a leash all the time. https://www.nps.gov/lavo/planyourvisit/pets.htm

From my understanding, you can bring dogs into the park, wherever your car can go, but not on any trails.