Back in the olden days, I would just drive the A12 to Civitavecchia, then ss1 to Montalto di Castro. What you propose from Tarquinia should work. You would still néed to get from the airport to the Auralia. SS1 from Civitavecchia is a fast(ish) 4 lane highway. I'm not sure, but it might have a decent shoulder. Check it on Google Earth and zoom in close to see.