We are planning a trip ti Portugal in the spring with our son and his family, 4 adults, and 8 and 6 year old boys. We've been discussing spending a week in Lisbon and a week in Porto. We don't want to have a car in Lisbon but are wondering whether it would be best to take the train from Lisbon to Porto and be without a car while we are there or to rent a car and drive to Porto keeping the car for our stay. Also, we would need a pretty big car, another factor to be considered.
There is no need to get a car just to drive between Lisbon and Porto. The train is pretty easy. The only issue is that you can't get directly from city center to city center by train - a couple of changes will be required. In Lisbon, you'll need to get to either Oriente station or Santa Apolonia station to catch the high speed train north (I took a direct subway from Restauradores near Rossio to Santa Apolonia). And in Porto, the high speed train will drop you at Campanha station, and you'll probably want to stay near the center, so you'll take a short train from there to Sao Bento station. (The latter train connection should be included in any ticket you buy to Porto.)
A car would be more useful if you want to stop along the way going north. There are some very worth towns to visit. Three examples of places I stopped: Tomar, Nazare, and Coimbra. I didn't drive, though - I used trains and buses, but I was alone. And in Porto, you may be interested in visiting the Douro Valley, and a car would be helpful for that.
FYI, I wouldn't arbitrarily choose one week each in both Lisbon and Porto. Lisbon is much bigger and, in my opinion, has much more to see and do. Porto is smaller. I personally would not want to spend an entire week there. I could imagine spending a week in Lisbon, easily.
You don’t need a car for either Lisbon or Porto and there is a good train service between the two. However, if you wanted 6 or 7 nights in Lisbon and were then to hire a car, there are some beautiful towns such as Evora, Tomar, Alcobaca etc that you could spend 4 or 5 days exploring, then have 3 nights in Porto.
You could always hire a car for a few days exploring on your own if they wanted to head straight to Porto, as it is going to be difficult to find a car for 6 plus luggage.