Welcome to the Disney Parks Moms Panel, Haruka! I just made a trek similar to this in June with my family when we stayed at Disney’s Contemporary Resort!
When I stayed at the contemporary, I was able to walk my family over the Magic Kingdom bus terminals, and hop a small shuttle to Boardwalk. Due to your resort reservation, that will not be possible. You’re right that busses will not run straight from
Disney’s Art of Animation directly to Boardwalk, but you have a few options! First, you can called a Minnie Van, which is a new service Disney offers for direct, safe and private transportation for guests on property. They offer car seats and at the last time of publicity, were about $20 flat to hire. You can alternatively call for an UBER, which will have car seats in Orlando if hired under the UBERFamily option. Check the
Parks and Hours calendar for Disney’s Hollywood Studios. Buses will start running about an hour earlier than park hours, and you may be able to take a watercraft from there to Boardwalk. I would check with your Front Desk Concierge for further advice on how to travel to
Trattoria al Forno and Disney’s Boardwalk Resort. They have have extra insight from your resort to your destination.
If I can help you further, please let me know. We’re all hEAR for you! ~ Lindsey P.