Hi Marlene! Unfortunately there is not an easy way to reach Downtown Disney directly from the parks. You would need to catch a bus at the park to Saratoga Springs or Port Orleans and then transfer again at either of those resorts to catch the Downtown Disney bus. That can take anywhere from 30-45 minutes. You also have to add wait times to that figure so it can easily take an hour.
If you have your own car you can drive to Downtown Disney but when it's time to return you will need to park, take the tram, then catch the monorail or ferry boat which is going to be tedious and take time too.
I would suggest you find a dining spot in the park or at one of the nearby resorts such as the Grand Floridian, Contemporary, Polynesian, or Wilderness Lodge. This will be less stressful for you and your family.
You did not mention the date so I was not able to know about the time of the fireworks. You can click
HERE to reach the calendar page for the Magic Kingdom. Set the correct month and then click on the day you are considering and the entertainment schedule times will show which includes the fireworks and the parades.