August in Sicily

I would subtract time from Taormina because it's too small to fill up 4 nights worth (unless you do side trips) and add to Siracusa or elsewhere (Ragusa was my favorite place, but it's quite hilly). Also beware of the heat. I went there in early September and it was blazing hot some days, so you may want to take it slow with an elderly parent.

I agree with Agnes: Beware the heat, and shift a night or two from Taormina to another spot.

One possibility would be your interior location. In addition to Vallelunga, you could visit Piazza Armerina and the Villa Romana del Casale, which has fabulous mosaics.

While in Siracusa or Ragusa, you might also visit Modica, Noto and Scicli.

Just a thought, we just spent 2 nights in a wonderful b&b in Lido de Noto- Terre dei Limomi. It was set in a lemon grove and had 2 pools. The private cabins each had their own kitchens. It was very close to the ocean. We went into Noto a few times, which was beautiful.

Sicily is very close to Africa.
Sicily in August will be an oven.
So plan altitude: visit Mt Etna’s volcano or the high town of Enna.
Or plan beaches: Ortigia has a small beach, boat ride around island, or Cefalu or the Aeolian islands.
Taormina is a one day trip tourist trap town -
Though the pebbly beach at its base is nice.

We're aware of the heat situation, but there's nothing we can do about that now, except expect it and plan accordingly.