My hunch is, if they did do something like a petting zoo, it would be done in a way where a handler brings out an animal, one at a time, and people wait in line to touch it and get their picture taken (like Raptor Encounter).
Times and what dinos for each time could be listed on a board, same way SeaWorld does meet the handler times. This way people could be guaranteed a chance to see the baby Triceratops they already have. (Rather than catching it by chance roaming the park.)
They could either add more dinos or just start with the Trike for now. Hopefully the little area would be themed well-enough to give a feeling that more animals are living back there too. Sound effects and a closed stable with mulch on the ground would be good enough to create the right atmosphere (and cheap enough to pull off without breaking the bank).
As cool as a ride-able dino for little kids would be, just like in the film, I would guess that's not a direction a project like this would go in. Too expensive with way too small a throughput.