I've not had a driver for that route, but I did hire one from Trapani to our B&B  near Agrigento, with a stop for a long lunch in a great restaurant in PortoPalo di Menfi; the price was 230 euro in 2023.   The car was a new Mercedes van.
The driver did not speak English; perhaps having an English-speaking driver would cost more but we did not need one.
So figure about the same; Palermo is further but you do not have to include the lunch stop. 
If you are interested I will give you the name of the driver.   I had checked prices with a few companies and the driver recommended by our hotel in Trapani charged much less than those I found online by myself.
From Agrigento, we hired another driver to take us to Licata, with a stop at Mandranova olive oil azienda.
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We got around on that trip solely with private drivers.