3 nights to fill between Porto and Lisbon

How about Nazaré?

There are many places that would be good for three nights. Coimbra is one of them. Conimbriga outside of town is an old Roman settlement with amazingly intact mosaic floors. But, not certain if your boys are old enough to appreciate it, though.

São Martinho do Porto is a small town with a great beach for children. It’s on a large horseshoe bay so the water is very calm. Ideal for children. From there, you can day trip to Alcobaça, Batalha, Obidos and the aforementioned, Nazaré. I like São Martinho much better than Nazaré because it’s not as much on the mass tourism route.
Ericeira is another lovely town with great beaches. It’s closer to Lisbon and a big surfer area. So, the beaches aren’t as good for small children.
FYI - there are forests around Sintra if you can’t fit in Bacaco.

I am with Kathrynj on this one. I am not fond of Nazare.

Inland Portugal can be very hot in the summer.

Another possible base is Caldas da Rainha, a traditional town with many tiled buildings but only 5 miles from the coast at Foz do Arelho. With a car, it’s easy to combine beach time with seeing the pretty towns nearby such as Obidos, Alcobaca or Batalha.

We agree with Kathryn, Nazare is a fantastic place and the boys would enjoy the light house and the walks on the beach as well as watching surfers.

Your overall structure looks great. I can only comment on where we visited on our recent trip (see my post), but your instincts are correct about Coimbra. My wife and I thought the university was a highlight of our overall trip, but our kids were indifferent and Coimbra itself is just a smaller version of the cities you're already visiting. So I highly encourage you to put something more rural / beachy in the middle. As you said, that could still mean basing in Coimbra and then venturing from there, but during the summer, the beach seems pretty logical. Depending on where you stay, you could even consider a daytrip to Coimbra (if the university interests you).

Evora. One day trip though.

Alentejo area is beautiful and well worth visits. Try Monsarez, Evoea, Arraiolos. Also, Viseu, Braga, Guimmares. Aveiro is very nice as well and don't forget Costa Nova with the striped painted houses.