Hi Michelle,
Welcome to the Disney Parks Moms Panel!
Disney's Grand Floridian Resort & Spa is one of my favorite resorts with access to the
Resort Monorail. While you can use the monorail to get to Magic Kingdom and Epcot, the complimentary
Resort Transportation to Disney's Animal Kingdom and Disney's Hollywood Studios is
Disney Bus Service. As you mention,
Disney's Minnie Van™ Service is another great option because it will take you directly to the park. My family used this service on our most recent visit so that we could get from Disney's Contemporary Resort to our pre-park opening dining reservation at Tusker House Restaurant on time.
Another option would be to try Uber or Lyft services. On my last visit, I used Lyft to get from Disney's Hollywood Studios back to Disney's Contemporary Resort after spending some time in Toy Story Land during evening Extra Magic Hours. On a few occasions in prior years, we also used taxi services, but those were typically more expensive than Uber or Lyft.
Michelle, as you consider your transportation options, be sure that you have downloaded the My Disney Experience Mobile App. The App has a great "Get Directions" feature that provides transit options and estimated transit times between locations.
Be sure to allow plenty of travel time between locations. I suggest an hour and a half to be safe!
Magic, memories and Minnie Mouse hugs,
Donyell