Don't misunderstand me, but you need more detailed information than you have, maybe from a guidebook at your public library: Sorrento is built on a cliff, and has exactly one beach, which is postage-stamped size, and located directly between the two Sorrento marinas. It has a strong diesel fuel odor at all times. The larger Positano beach is pebbles, and is requires a downhill ramp and a few stairs from the nearest sidewalk, which I think is 50 m from the road. (Not sure about that.)
Towns like Positano and Amalfi have precisely ONE two-lane road running through them. I saw a post (long since our last visit) that suggested that this road is one-way in the high season. But I don't know if that is true. (You have not yet given your month of travel, have you?) I personally would never visit this area without air conditioning in my hotel room.
It happens that Ravello, while even harder to get to than Amalfi (and that's saying something) is much more suitable for a visit by wheelchair. The chair will be necessary, for the distances to cover on pedestrianized walks. However, because Villa Cimbrone, and the associated hotel, are tourism destinations, it may be possible to be driven to it. The views from Ravello are quite lovely.
I didn't put your address into Google Maps, but are you planning to use the Circumvesuviana train for transportation to Sorrento? There is an elevator in the Sorrento station, but does your family have any, lifetime, experience with ... public ... transportation? I feel confident that someone will get up from a jammed bench to give your father a seat, but sometimes the train is too full to see the bench from the open doors! We paid 15 Euros in Sorrento for a cab from the Circumvesuviana 1/2 mile to our hotel, which I thought was a ripoff. If you have to use cabs that aren't based in your town, you may run into some money. But you are RIGHT not to rent a car. It's an albatross in this area, parking absolutely HOPELESS from Sorrento to Salerno on the coast.
I guess you're hoping for a package tour. I urge you to consider a hired car for a day. That way the pace will exactly suit your father, instead of having to keep up to a list (and pace) that was promised to four other people in the van. I believe your father will be unable to reach the funicular near the Capri marina, which is quite large, with 1/4 mile walk to the farthest dock. So he'll have to start out with a cab from that level. This is a challenging itinerary for him.