Where to go…

It helps to know how much time you will have for your trip and what your family's interests are.
Is your 10yoa child mature enough for Anne Frank? I took my son there when he was kind of a young 12, and he was fine. The situation is presented in a way that is accessible, but 10 is young. I'd say if you think that child is too young for it, wait. Or plan to go back. If you do go, be sure to take the kids to the Sam and Julia Shop, also known as the Mouse Mansion.
If the 10yoa is mature enough for Anne Frank, they can also handle the Atlantikwall Museum near Ostend in Belgium. The coast there is very nice. We did it as a day trip from Bruges, but if I had it to do over, I would have stayed on the coast and also visited the aquarium (my kid was really into aquariums and car museums) and day tripped to Bruges.

Consider Portugal. So much history in a relatively small country from dinosaurs (Lourinhã) to standing stone circles older than Stonehenge (near Évora) to Roman ruins (Conimbriga) to the "discoverers" (Belem). Plus beautiful churches, unique tile decoration, walled towns with castles (Óbidos), and amazing food. And we didn't even make it to the Algarve or Porto.

https://community.ricksteves.com/travel-forum/trip-reports/the-netherlands-belgium-april-2024-brought-the-rain-pants-needed-the-rain-pants

Maybe my recent Trip Report will influence you. September weather should be much dryer than our April Trip, but we did get Tulip Season.

Whatever you decide, have a great family adventure!

There are all kinds of gems you haven’t been to or mentioned. But you can’t see them all so choose what is calling to you. I love traveling in September and have spent that time of year in Poland, Budapest, Montenegro, Bosnia, Croatia, Slovenia, and the Baltics (adding Romania this year).

I am sure Belgium and the Netherlands and Paris would make a lovely trip. It might be less of an “outdoor” trip but somewhere (if you search) is a trip report by Hank on cycling through some of this area.

I love the Low Countries and think you'd have a great holiday there- interesting cities, lots of art, beautiful countryside (of course including the windmills), and in my opinion the best beer in Europe, if that is of interest. Regarding the question about children visiting the Anne Frank house, I read the diary of Anne Frank when I was 11 so I think it would be age appropriate for 10/12 year olds. She herself wasn't much older when she wrote it.

Go where you haven't been. You haven't been to Spain, Portugal, Greece, Croatia, Turkey, Scandinavia, Egypt or Morocco.

If you pick Spain, consider this:
Barcelona 4 nights; high speed train to Madrid; four nights in Madrid with day trips to Toledo and Segovia; train to Cordoba, 2 nights there; train to Seville, 4 nights there; train to Granada, 2-3 nights there; train to Malaga and Rhonda, 3 nights there. Fly out of Malaga.

With three weeks and a car, I think of no better place to be in September than Slovenia and Croatia. They tick all your boxes. Everyone speaks English readily, food is amazing, mountains rival Switzerland and glorious architecture.

Thank you all! @emily I am liking your idea of Slovenia/Austria or Slovenia/Croatia. I think you all may be right in saying that the Low Countries may not provide the nature that we are looking for.

We were in the Low Countries this past April, and spent 90 % of our time outdoors. Walking along the canals, canal cruises, spectacular Kinderdijk, and biking. Because of weather, we couldn't bike to the coast from Haarlem, but it's on my bucket list. The Dutch are hardy folks, and spend a great deal of their life outside. Please don't rule out the Low Countries. The people are incredibly friendly, speak excellent English, and the area isn't as expensive as other countries. It's very comfortable being there, safe, clean, organized, and there's so much more to the NL than Amsterdam.
However, you have no bad decisions.
Safe travels!

Thank you for your insight! This is a tough choice!!

Normandy would be a great add to the Low Countries trip.

Another vote for Slovenia & Croatia.

Another vote for Croatia and Slovenia, and you can also add in Montenegro (Bay of Kotor) as a daytrip from Dubrovnik. Or spend a couple of nights in Montenegro. September will be warm enough for swimming in the Adriatic, if your kids are interested in some beach time. But not unbearably hot.

And Spain would be great, too! I love, love Andalusia. There is history and beautiful architecture and delicious food. It will still be hot in September, though. Not sure how you feel about the heat. Or you could visit Barcelona, Costa Brave and the Pyrenees. Might be cooler and you would see lots of nature.

Definitely visit some place new!