August 2022 - Belgium, Netherlands or Both?

If you want to avoid repacking, I would not do both. The food is better in Belgium, although international food in Amsterdam is OK. There are some parallels between the two countries, but you won't have time to think about them during your first days in each. I personally think that the base cities of Amsterdam and Antwerp (which I much prefer to Brussels) have enough unreserved train daytrips that you can choose whichever has a cheaper flight home. (There used to be a direct bus from the Antwerp central train station to BRU hourly. But there's fine train service but often with a change in Brussels.)

Considering Den Haag/Delft, Leiden, and Utrecht (each of which is hard to do in only one day), there may be a slight edge for the Netherlands. While Antwerp is not quite as rich a destination as Amsterdam, it's good for several days. I would NOT try to visit both in a single week. Note that August is vacation month in Europe and there may be some closures or shorter hours. I would want air conditioning at my hotel.

Perhaps I should say that Amsterdam and Antwerp have some of the same contemporary urban ills, like homeless, vacant stores, and a drug problem. Not reasons not to go, just mentioning. There are a host of old posts here (search box top center) about which city to base in for Belgium. Example:
https://community.ricksteves.com/travel-forum/belgium/day-trips-from-brussels-besides-bruges-and-ghent

Also a note to mention a lot of "hidden" (I don't mean "undiscovered") attractions in Belgium. I mean like the Beguinages besides the most famous, in Bruges, or the Cogels-Osylei townhouse district in Antwerp, or the huge open-air sculpture garden in Antwerp. I recommend Lonely Planet for whichever country you choose. There are a few Sunday only (well, pre Covid) tours to book at the TI, like Antwerp or Leuven city hall interiors. Otherwise, off limits. There are also smaller cities in Belgium that are gems, like Lier and Leuven. If you are staying in Antwerp (spur rail line ... ) you can do Lier and Turnhout the same day. But you have to know about the Art Deco city hall and the superb wood carvings in the Turnhout cathedral.

If you can be in Brussels between Thu, Aug 11 – Mon, Aug 15 you’ll see the flower garden at Grand Place. If you have a week, you can visit both countries and spend time in Amsterdam, Brussels and Bruges.
You can fly nonstop from Edinburgh (EDI) to Amsterdam on Easyjet and KLM for less than $100. Since Easyjet is a low-cost carrier, they may have a stricter luggage allowance than KLM. Ryanair has a nonstop flight from EDI to Brussels for less than $50. You can take direct trains between Amsterdam and Brussels (3h) and between Brussels and Bruges (1h). Bruges makes a nice day trip.
I too suggest buying Lonely Planet guidebooks because their Amsterdam 13th edition will be available in May and their Bruges & Brussels 5th edition will be out in Mar. Rick Steves new editions come out after you return.

With respect, ten days is a very, very short visit to Scotland. You could easily spend the additional week in Scotland, doing some combination of arriving early (spending extra time at or near the tour's origin point), staying on in Edinburgh after the tour ends, and visiting places the tour skipped. This would give you more sightseeing time and less travel time, and it would reduce the risk of COVID-related travel hiccups.

I spent 26 days in Scotland in 2019 and felt constrained in choosing my destinations due to the limited time--though admittedly I was traveling independently via public transportation, without the logistical advantages of a tour. My travel mate, who had only 19 days in Scotland, was even more frustrated.

Keep in mind that Scottish weather, especially in the west, is unpredictable and tends to be wet. You can't be sure conditions will always be good for outdoor activities, which are a big part of Scotland's charms. Therefore, it's best not to plan a bunch of short stays in many different places.

Edinburgh + August = FRINGE

Thanks for the advice. I totally understand that our time in Scotland is barely enough to scratch the surface, but I have been there before and we are going primarily so my dad can see the military tattoo. After considering your advice and doing some of my own research, it looks like we are going to commit to the Netherlands for the full week after Scotland. I appreciate all the help and you will likely see me on the Netherlands forum with questions about itinerary and restaurants.

Nigel, I did a little research on Fringe, but don’t think I fully understand it. How crazy and interesting will Edinburgh be during that time?