Most engineered floors can be sanded. Most. Doesnt mean yours can. But it requires a pro. First step is to call and set up a bid.

Cut your dog's nails. They are too long. And think about putting in tile. There are zero wood floors that will warrant with pets. A haandscraped hickory is about as good as it gets at disguising wear.

There is such a process that hardens wood flooring. However, it cannot be done to an existing installed floor. The only domestic wood floor product that will resist denting is acrylic impregnated wood flooring and it is not readily available nor cheap.