4-6 week trip with two kids, 6 and 3.5

We went to Spain with our kids when they were 7 and 9, and visited a lot of playgrounds - some on purpose, some when we saw one in a small square. I originally tried to keep everyone awake when we arrived with a walk over to Retiro Park, but the kids were falling asleep standing up and that's how we found out that we prefer a nap (just an hour or two) after the overnight flight and then get up and go find food or walk around before sleeping for the night. Having a vacation rental with a kitchen was helpful - try to have fruits and vegetables that they will snack on because our kids didn't order salad at that age. Don't get them too excited about getting off the airplane - you will still be in the airport EES lines and maybe a taxi. But overall, they adjusted to jet lag well and we traveled by train and bus (which is when I found out one kid gets motion sickness and talked to a pharmacist) and went to cathedrals and museums).

Thank you! Noted on the nap and then walking around. The flight we were eyeing is a morning arrival, so assuming we book accommodation with a decent check in time, we will try that. I’m wondering if we’d have better luck booking a hotel that may offer early check in for that reason upon our first arrival.

OP, what I've learned here is that a lot of folks book accommodation for the night before and let the proprietor know that they will be arriving in the morning. This way, there's no issue with availability of early check-in.

In 1981, I took a job with the Army Corps of Engineers in Saudi Arabia. My daughter was 11 and Son 5 1/2.

Enroute to Riyadh, we spend three days in London, or firs experience at touring Europe. Every year we toured foreign countries at least once.
We didn't spend time at beaches or visit the French Disney or stuff like that. We did the typical tourist things visiting historical places, museums, etc.

We did find that my Son, visited a museum like the Lourve at 7 1/2 that he was ready to leave after half an hour. Still, he hung on and we did see quite a lot, although late in the day, I would have to carry him. I do remember when we entered the Sistine Chapel (same trip, he was 7 1/2) that he was in awe of the place and wanted me to explain all the frescoes on the walls and ceiling. Back then, there was no time limit in the Sistine, so we stayed 45 minutes, sitting on the floor looking up mostly at Michelangelo's masterpiece.

As for you daughter, she loved the history and art and we had no issues with her.

As for a 3 1/2 year old, I expect that would be more difficult for museums. Still, young kids love some touring. My Son loved the boat ride in Venice, going up the Eiffel Tower and the Roman Coliseum. Now both kids are in their 50's well traveled and still love to travel.

You probably would need to arrange for an afternoon nap time for the little one.

Thank you all for your feedback! After a lot of research we have changed up our plans to focus on Spain. Barcelona > Valencia > Mallorca > Madrid. My idea of Mallorca was to add a resort stay to give us a break from city exploring etc.

Oops, I see the ages in the title!
Do as the Spaniards do, rest and nap after lunch and enjoy the cool late evenings and later dinnertimes. The kids will adjust to the schedule differences, as will you. They can get back on US routines when you return. Siestas (especially in the hot summers) rule! Be sure to get AC at your lodgings.
Oh yes, in Madrid the kids may get a kick out of the vertical garden "Jardin Vertical Caixaforum". You will all like the hot chocolate with churros for dipping, and the Spanish tortilla de patatas (a kind of frittata with potatoes).

You probably already know, but the Sagrada Familia is one heck of an architectural wonder. It is magnificent to behold and worth the cost and wait. And the kids will love Park Guell in Barcelona also. Don't miss them!