1 week itinerary for Portugal in April

I wouldn't bother with the drive to the Algarve. Especially in April (off-season). With 7 people and the associated logistics, I would happily stay in Lisbon for the whole duration. For instance, Evora is an easy day trip by train. And there are plenty of other day trip options.

You can take the train from Rossio Station to Sintra. Instead of going to the Algarve, you might consider Cabo da Roca (great hiking) and Cascais in addition to Sintra and Evora. We found Obidos to be really beautiful in the spring. If you do go there, just walk by all of the touristy gift shops near the entrance.

Unless you're a big Henry the Navigator fan, Cape Sagres and the Algarve in April isn't the best place to be -- windy and chilly. There's enough to see to spend an entire week in Lisbon, but if you want to get out of town for a day or two, I'd suggest Evora, or for a different direction entirely, consider Mafra. The National Palace is an architecture destination--it's gorgeous and there's also model of a small traditional village. It's only about 45 minutes from Lisbon by bus. Evora is accessible by both train and bus. Unless your flight is very early on Friday, you could stay one more night in town. It's easy to get to close-in Portela.

On Tuesday you can also take a direct bus from Lisbon’s Sete Rios station to Lagos (4h) and take a taxi to Portimao (8-miles from Lagos) and rent a car.
From Lisbon’s Oriente station you can take a direct train to Évora (1h 45m) for the day.

I too would scrap the Algarvein your timescale. Unless you take the boring toll road, getting a car and driving to Lagos would fill an entire day with a few short stops for lunch and coffee along the way.

Covering Sagres to Tavira isn’t practical in one day unless you want to spend the entire day looking at tarmaced roads. If you must include the Algarve, then spend this day driving the loop from Lagos up into the Monchique hills then head over to the stunning west coast around Carrapateira then see Sagres and the Cape. Scrap Salema, as the beach is better at Carrapateira with its stunning cliffs. These days, Luz has a better selection of cafes and restaurants than Salema.

Seven people plus enough luggage space sounds like a large vehicle that would be difficult to park. Consider 2 normal sized cars instead.

Instead of the Algarve, I would spend longer in Evora and also see Cascais from Lisbon.

Thank you so much for this valued input. We have never been there and so we follow the guidelines in the book. Is Porto worth a couple of days?

Oh, yes, it's really worth it. It's a different vibe from Lisbon, smaller, homier. It's a good walking town, too. See the Bolsa, Ribeira, visit a port wine house. Easy to spend a few days there.

Porto is worth a visit, but are you able to fly out of Porto so as to avoid using your limited time returning to Lisbon?