I'd suggest an Uber/Lyft to Universal.
As far as doing it in one day, you can hit the highlights but you'll have to skip out on some things (e.g., there probably won't be time for the live shows, Seuss land, the entertainment and shops in Diagon Alley/Hogsmeade, and a few of the "lesser" rides) - and as others said, you're going to need Express Passes to maximize your efficiency. To get you started, here's a good touring plan (you'd have to add in the new Hagrid ride, as desired):
https://orlandoinformer.com/universal/studios-islands-adventure-1-day-touring-plan/
(Honestly, if it were me, I'd add a day to my vacation, spend 2 days at Universal - which
is enough to see everything you want at a more enjoyable pace - and spend the night in between at a Universal "premium" onsite hotel. The cost of the hotel will probably be less than a single day's worth of the Express Pass ticket upgrade for the family, and would entitle everyone in the room to unlimited express passes the
entire day of check-in
and check-out, so you wouldn't have to purchase it separately. (Unlimited Express Pass for everyone in the room is an amenity offered by Universal's 3 premium onsite hotels - the Hard Rock Hotel, Portofino Bay and Royal Pacific Resort. For my family of 4, that's well over a $400/day value -- less than the cost of the hotel room itself!) But you may not want to spend that much time, and unpacking/repacking to switch hotels is always a hassle...