Sorry. As stated in your other post, there is no way that I would try to cover the Douro and the Algarve in a trip the length of yours so this drive wouldn’t happen.
The “coast “ road doesn’t hug the coast, bit is more interesting as it passes through places rather than being a motorway, but it will take you hours. I drove in May two years ago from an hour south of Setubal to the Algarve (check out Google Maps) and this took us over 5 hours with a short lunch stop and one quick diversion to look at the coast. This about a quarter of the distance that you are planning on driving in one day.
I urge you to consider visiting the stunning beaches closer to Lisbon to make the trip more enjoyable for all.