I work with special needs preschoolers and we have a few techniques for tantrums and eloping (the technical term for "running away") that can work for any child. First, all of the adults have to be on-board and commit to using the same consequences for each and every incident. Disneyworld is not a good place to introduce new behavior management techniques, so these should be implemented and practiced before the trip.
At 4, she should be old enough to understand what is expected of her and what the consequence will be for poor behavior. She needs to be told the "rules" in advance and they should be kept very simple. 1) You must ride in the stroller, hold someone's hands or be on the harness at all times. You may not run away from an adult at any time. 2) If something is wrong, you may not scream or cry. You need to use your words to let us know what the problem is. If you want to do something, you must use your words to ask us.
Anytime she violates the rules, tell her quickly, firmly and with very few words what she did wrong (you ran away from Grandpa and that is not safe). Place her in a time-out wherever you happen to be. Take her to the nearest out-of-the-way spot you see. It might be on a bench, in a corner, by a wall, etc. If she refuses to stand or sit still for her time-out, keep an arm around her or loosely hold onto her wrists. If she is screaming, do not talk to her. Above all, do not lose your cool. If she's quiet for a moment, simply say, "You need to calm down. Then I will talk to you." Eventually, she will get the picture and calm down. Repeat in a few words why she had a time-out and tell her what you expect from her: "You had time-out because you ran away from Grandpa. That is not OK. You need to stay with us all the time. Do you understand?"
Besides just giving consequences for poor behavior, be sure to reward good behavior. If she points and says, "Can we ride the elephants?" Say, "Of course we can! I love how nicely you used your words and asked!" This will make her proud and teach her that good behavior comes with rewards. Be prepared to follow her lead and let her choose what you do next if she asks in an appropriate manner. If she's riding along nicely in her stroller, frequently tell her how well she's doing. Make a big deal of it so she'll get the message.
If it were a grocery store or restaurant near home, I would recommend being prepared to remove her immediately. However, if you're in the middle of a park, you've made a huge monetary and time commitment to be there. Sending her to the hotel with grandpa is sure to make her sad, but she might not equate the behavior with the punishment. Practice the time-out technique as much as you can before the trip and keep reinforcing good "Disney behavior." Hopefully she'll realize it's a lot more fun and rewarding to act appropriately and that positive attention is much better than negative attention. Good luck and have a great trip!