Hi Carrie,
It sounds like you have Magic Your Way Base Tickets. These tickets allow you to visit one of the theme parks as many times as you like in a single day. You can visit Magic Kingdom in the morning, go back to your hotel, visit an off-site location, etc. and then return to the Magic Kingdom that same day to catch the fireworks, ride some additional attractions, etc. With a base ticket, you would not be able to visit a different park in that day, even if you wanted to enter the park just to dine there.
If you were interested in visiting another park in the same day, you would need to purchase the park hopper option, as you discussed above. I've attached the link to the Disney World "tickets" page, which provides additional information and current pricing on all of the ticket options. Click
HERE if you would like to visit it.
If you wanted to do something different on the day that you are visiting Animal Kingdom, you might consider making dining reservations in the Downtown Disney or Boardwalk areas. Neither requires theme park admission. The Boardwalk has tons of free entertainment and many wonderful dining options. Downtown has amazing shopping and dining, including an unbelievable Lego Store that delights kids and adults alike!
Have a wonderful trip!