This plan is workable...However, you must arrive in Sintra before the crowds get there. The small parking area I have used a few times is across the street from the train station on Rua Joao de Deus. You pay the machine for a ticket to put on the dash to keep the car there, but return by around 5:00pm. The machine has a note on it explaining the cost and times...I think it only accepts euro coins, but I could be incorrect. The best part of parking here is the bus to take you around is a 2 minute walk away at the train station, the first and last stop. So you have to pick up the car early in Lisbon and be on the highway by 8:30am the latest. If that lot is full, there are other lots to use as shown in the guidebook, but involve more walking to get the bus.
Don't skip Obidos, Alcobaca, or Batalha, especially for the sake of your kids. As much as I love Lisbon, there is so much more to Portugal than the big cities. The best part of Obidos for us has been walking on the massive wall protecting the village. To think soldiers so many centuries ago walked these same walls is just incredible.
Before heading to Alcobaca, make a quick stop in Sitio, above Nazare. The view from the cliff overlooking Nazare is gorgeous. Try some peanut cookies from the vendors there. It only costs about 3 euros.
Batalha is even worth 1/2 hour for a quick visit. This church, and the huge bronze statue outside, has to be seen at least once to be believed that humans could construct such a building so long ago.
Alcobaca has important historical significance for this country and can keep you occupied for a couple of hours. Coimbra is also an integral key to understanding Portugal and its history.
Porto has much less meaning without the "Driving the Douro" chapter. Visit a winery where the vineyards are to comprehend the rough landscape producing these special grapes. The soil is not what we thought it would be, you'll see.
July will be HOT and sunny in all the places you will be visiting, so hats and sunglasses along with plenty of water bottles for the girls will be important, and for the adults as well. Crowds will be a challenge as well, as Portugal is becoming very popular.
I have never used the train in Portugal because a car allows tremendous freedom and efficiency. With a good GPS map and the VIA Verde transponder in the rental car you will be fine. If you can "Drive the Douro" on day one for Porto before going to your hotel, you can drop it off later that night to save rental and parking costs. You do not need a car in Porto for the next two days before flying out.
Follow all the advice in Rick's Portugal book for these places, as his instructions are definitely on target.
Good luck