Welcome!!!
I believe there's an app for comparing Uber and Lyft on the fly, I downloaded it a while back but never used iit so I deleted it. Might be worth looking in to for folks who like to compare.
For a nap, I think I would either Minnie Van or use the rental car because of the car seat situation. A regular Uber or Lyft won't have a car seat for your small fry. Another thought is to bring a nice comfy stroller that fully reclines, then he/she might be able to nap without leaving the parks. I'm trying to remember to way back when my DS was little and I'm recalling some naps in the stroller while we strolled around Epcot. I'm also recalling some earlier evenings, which is why having a nice big villa with a balcony is so nice - enjoy some grown up down time after bedtime