That’s a lot of 1-2 night stays which means you will be really rushing around and spending way too much time moving from place/hotel to place.
You could day trip to Evora and add another night or two to Lisbon.
With two nights in Tomar that means seeing all three places you mention in one day. It’s possible but not enjoyable. Each of the three monuments will take a couple of hours and driving on the smaller roads is easy but can be time consuming. And, while Alcobaça and Batalha have different histories, they are really fairly similar . Alcobaça is my favorite. Coimbra is lovely but could be done in a day trip if you arrive early.
You might want to turn your car in in Coimbra and take the train the rest of the way to Porto. I would spend all the nights in Porto and day trip to the Douro. The person driving wouldn’t get to really enjoy the scenery and there are many good tour companies for a day tour to the Douro.
And, lingering to enjoy long lunches and savoring the wine is a lot of what Portugal is all about. I don’t think you will get that ambiance with your current itinerary.