recommendations for 1 week in western sicily for large family group

Monreale for the mosaics.

I would avoid driving in Palermo under any circumstances. Merely being a pedestrian in Palermo is a challenge (and I really like the city).

I took an inexpensive evening cooking class in Trapani in 2015. Don't remember the name of the place; I just spotted a flyer at a local travel agency. We prepared homemade pasta and Sicilian-style pesto. But you might be able to get someone to go to your villa and teach there, and in that case you'd probably have some input into the recipes being taught,

No problem picking up a rental in downtown Palermo by the dock area. As long as you are on the ‘modern’ streets all us good. We had stayed in Palermo for 3 nights, then picked up the car and drove out not to return.

In 2014 I went with a friend to Sicily. We rented a car from Hertz in Palermo, in the newer section of the city. We were very concerned about getting out of town, but it turned out that we only had to make a few turns on easy streets to get to the surface road to Monreale (which we took) or the highway out of town.

The next year, my friend returned (with his husband instead of me) and they rented from Europcar next to the Palermo train station. He told me that it was also not difficult to get out of Palermo from here.

In both cases, locals strongly advised not trying to drive in the old section of Palermo, but in both cases it was not necessary. We had GPS (brought from the US), which definitely made it easier.

If you need an automatic, you have a far greater likelihood of getting one at Palermo or Catania than anywhere else.

You could add Segesta (and see the beautiful Greek temple and theater) onto to your trip to Castemare del Golfo (which is lovely by the way). It is easy to rent cars at the Palermo airport. The airport is far from the city center and you don't deal with traffic.