16 days Spain itinerary with 5 & 8 yrs old kids.. Max 3 stops

My suggested day trip from Madrid is Segovia. It’s easy to do by train or bus. The kids should be enchanted by the ancient aqueduct. You likely will, too. Isabella’s castle is there, too, from before she married Ferdinand, became queen, or met Columbus.

If you were to add a fourth place, make it Granada. But keeping it to the three you mention keeps things simpler, as you said.

Not sure that I would want to do 6 nights in the Canary Islands. We did one day there while on a cruise and enjoyed it, but 6 days, NO.

Day trips from Madrid should be Toledo and Segovia. Seville is great and at least a day in Cordoba. Malaga is OK, but not one of my favorites in Spain. The Costa del Sol beaches are not that great.

For me, with 2 kids, flying from Madrid to Tenerife and flying back to Seville, or whatever combination you plan would not be ideal. The fewer flights I would have to take the better. There are nice beaches in Barcelona or other places along the coast. So I have read here since I am not a beach person.
In Barcelona the children would enjoy the Maritime Museum which has an exhibitions geared towards children and Park Gueli is another choice.

Why are you including the Canary Islands? Its way out there...
Two itinerary suggestions:

Both major cities, their surroundings and Andalusia
Barcelona & coastal areas (5-nights)
Madrid (incl Toledo & Segovia)(5-nts)
Seville or, Grenada (6-nts)

Both major cities, their surroundings and Basque Country, this trip will offer more seaside actives for your little ones.
Barcelona (5-nts)
Madrid (5-nts)
San Sebastian or, Bilbao (6-nts)

Thanks a lot to all for the help and input.

I think Madrid, Seville and Barcelona would make a great trip.

I can see that the Canary Island would be a bit off the track and we would lose time in traveling.

We are vegetarian (no meat or eggs. Ok with dairy). Appreciate it if you could share some options for eating out.

Note that Catalunya has declared a water emergency due a multiple years long drought, so there could be limits on water usage in Barcelona. Don’t count on pools being open or fountains to be turned on.