Yes on driving, and even some of the trails are wheelchair friendly great for young kids. The map they give you when you get here will lay it out. Easy tonfollow and ask anyone around they can guide you.in the right direction
The lodge is a great spot for strollers. There is a big lawn and had a bunch of very young kids playing. Try the riverside walk or the weeping rock trail; both paved. The shuttle is full time as of 3/10/18 when I was there recently. There isn't a bad view in the whole park so plenty of scenery. The east entrance is missed by many but is a great drive if you don't mind the detour on your way out.
The park shuttle may be running then so, depending on what day you come, you'll have to take that thru the park. Right now it's running weekends only, but will go full time by summer. It runs along "scenic drive" and stops at different points where you can hop on and off. If it's running, private vehicles are not allowed thru the park.
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