The dog is dancing together with the other dogs. The dog is dancing with the other dogs. Teacher .... you said first sentence is correct but I think 2nd sentence.

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Quition - Question

The dog is dancing together with the other dogs.
The dog is dancing with the other dogs.

Both sentences are written correctly in the present continuous form, have the same meaning and can be used interchangeably.
However, the first sentence “The dog is dancing together with the other dogs” puts more emphasis on how the dog is dancing and the way it moves which is “together, in harmony with the other dogs, their dancing is well-coordinated. 

The second sentence could mean that the dog is dancing with the other dogs but it doesn’t mean that the dog follows along all the dance steps and movements the other dogs are doing. He is dancing with them not minding to follow the exact dance steps.
There’s just a subtle difference in meaning and they can be used interchangeably depending on which one you are emphasizing.