Hello Natalie, welcome to the Disney Parks Mom´s Panel!
Visiting 3 Walt Disney World parks in one day is a very feasible and common feat.
The first thing that you will need is
Magic Your Way Tickets with the Park Hopper Option - the only way of visiting more than one theme park on the same day.
With Disney´s bus transportation system you will be able to move between the parks - even with you stroller.
Between Hollywood Studios and Epcot you will be able to enjoy a boat ride or a pleasant walk through Disney´s Boardwalk.
To make the most of your time I always recommend using your own or rental car. Parking at all Disney parks and resorts is free for guests staying at a Disney Resort.
Check
Disney´s Calendar to know park hours and events times, so that you can plan your day accordingly.
I can only say that Animal Kingdom should be the first park to visit.
Thank you for visiting and letting us help you plan a magical Disney vacation.
Hope to hear again from you.
Miguel