As someone else said, you don't need the reservations for rides, but what you'd want to do is pick three reservations for things that you+kid really want to do, and book them for later in the day when the lines will be stupid long without them (though again this can be very seasonal). You get to the park at opening, do all the other things you really want to do that you don't have a reservation for in the first 60 minutes before everyone else filters in, and then chill and do your reservations the rest of the day, watch parades, see fireworks, just take it all in.
Also have to be aware that the parks often have "extra magic hours", either 1 in the AM, or 3 in the PM. Meaning Disney hotel guests +Swan and Dolphin get the parks to themselves. This means that if you aren't in that group, you avoid the park that has the extra hours that day. And if you are in the group (staying at Disney hotels), then you get there for the extra hours and take advantage of the opportunity to have small lines.
All that said, Disney is not just rides, it is crammed to the hilt with stuff that most people are content to just walk by, but in any other context this same stuff would be a day trip in its own right. There is a 19th century steam boat, and steam train, that are among the finest in the world that you'll never wait in a line for and most people ignore, because they are too worried about getting on a 90 second ride with Peter Pan. There is an 18 story sphere that you could put in the desert and people would drive thousands of miles to see it, but for most people at Disney it's just an obstacle on the way to the Frozen ride. Kids love all this stuff. They will just be constantly in awe of it if their adult companions don't drive them to exhaustion and fits of rage over the toy they want. People who don't "get" Disney, are usually caught up in this misunderstanding of what it has to offer.
Rental car: Definitely not needed. Disney transport will take you anywhere for free, but it can be crowded, and the buses in particular can be slow. Especially for the cheaper hotels. That's where Uber can come into play. Should be less than $10 anywhere you want to go, and there are plenty of drivers. Rental car is only helpful if you want to go to Universal, Sea World, etc... and/or if you game the system by staying off property, driving to the Disney resorts within walking distance of the parks, and telling the guards you are "shopping".