Greece with a 9-year-old

Tough call.
If you stick with your original mainland plan you have to take into consideration jet lag and driving a car.

If you chose the mainland then I would suggest you change the order of your planned route. Drive to Nafplio. Its a couple of hours from Athens airport. Most of the drive is on a major highway with the last part on a good secondary road that meanders down to Nafplio. Find a hotel in the old town area. Nafplio is a great place to stop and recover from Jet lag. When we did a transatlantic (buy the way our trip is essentially the same as yours in time spent getting to Greece) we picked up our car, drove to Nafplio and didn't touch the car again for 2 days. Its a good thing that Nafplio has so much to offer.
From Nafplio I would drive south and visit Mystras (the last Byzantine city) at Sparti. Its a good site. Then continue to Monemvassia. Be sure to find a hotel inside the village walls. There is something special about sleeping in a period room from the 1400s.
If you choose to go to Kardamyli you will be fairly close to one of the best ancient sites in Greece. Messini.

Then start back towards Athens visit Delphi. Best strategy is to arrive mid afternoon and visit the museaum which will set you up for a visit the next day. Get to the site early and you will have it with just a few other people. When the bus crowds arrive the site is very busy.
Spending a night at Delphi is special too. Our hotel has a balcony where birds sailed by and we could see olive groves all the way to the Gulf. It resembled a river of trees.

Personally I would drop Olympia and on the way back to Athens stop and visit Ancient Nemia. It had sister games to Olympia and the stadium is still there. You can run races from 2,000 year old starting blocks. Many people drive right past Corinth but there are some interesting things there. There is ancient Corinth (biblical era) and right beside it one of the most impressive fortresses in all of Greece at Acrocorinth. Its a drive up fortress with 360 degree views. Of course there is the canal but if you take the path along the west side of the canal you will find what appears to be an abandoned machine gun nest, an abandoned rail line and bridge and on a rocky path scratches on the rock from the keels of boats that had to be dragged across before the canal was built.

You probably will want to have 2 or 3 days to visit all the ancient sites at Athens at the end of your trip.

Personally I don't think taking a short visit to Crete make sense with the priorities you have. Now if you wanted to spend 12 days in Crete I might have different advice.

Here are some images of what you are planning to do.
Nafplio https://www.flickr.com/photos/stanbr54/albums/72157632094108982
Corinth Area. https://www.flickr.com/photos/stanbr54/albums/72157711755443483
Peloponnese, Mani and Monemvassia. https://www.flickr.com/photos/stanbr54/albums/72157711323535897

I have a similar dilemma, only my children are older. I’m thinking of flying to Chania for about 7-9 days in Crete. In the past we have spent a night at an airport hotel in London to help with the jet lag and traveled domestic.

Chania town is quintessential European so it would be fun for your son to explore and the beautiful beaches are an easy day trip. One of our day trips will be to Rethymno and the “Homer” museum at Eleutherna with artifacts from a 730 BC funeral pyre and warriors shield that prove the description of Patroclus’ funeral pyre. I think my son will love this. After Chania, we plan to travel to Matala with stops at the Phaistos Minoan Palace (where Phaistos disc was discovered), Hagia Triada next to Phaistos where Linear A tablets, Harvestor’s vase, and sarcophagus were found). Gortyna, for Roman ruins to see where the the Gortys code was found (later became Sparta law), ending at Matala for the caves. We would then continue early in the morning onto Knossos Palace, home of the Minotaur. Knossos is partially restored, but will be a place I know my kids will love since they are also interested in mythology. We also expect to spend 2-3 hours at the Heraklion archeological museum which is the second most important museum after the archeological museum in Athens. I’ve been there before but didn’t understand the significance. This time it will be more meaningful. We will stay either in Heraklion or Archanes. We may add a day to go to the Diktaion Andron cave (where Zeus was raised) and the mythology park, even though they are gimmicky.

We also want plan to stay in Athens for some time, with DIY trips to Delphi and Nafplio, Corinth, Tiryns, Mycenae, Epivardos, Nemea, and Argos. You can rent iPads or VR glasses that show many of the ancient sites in 3-D, as they were. We dropped Ancient Olympia from our plans because it’s so out of the way. I’ve been there before and really enjoyed it. But, it’s hard to find decent affordable accommodations for five on that side of the Peloponnese and we don’t want to be driving hours and hours every day. If we drop Crete, we would extend our stay in Nafplio to Mani and explore all the mythological places there.

I’m not a Greece expert, as I’ve only been to Greece once. This itinerary may be garbage. But I hope this helps with your research.

I recommend that you do include Olympia! It was a highlight for us while Nemea was interesting but not on the scale of ancient Olympia where we spent a night. Our Greek friends strongly encouraged us to visit Olympia and we were so glad we did!

This is what we are settling in to:
Fly into Athens, drive to Nafplio, stay 3 nights. Visit some of the sites in the area including epidavros.
We were going to do 2 nights in Hydra, but decided to nix that and instead go to Monemvasia or 2 nights
Kalamata for 2 nights
-drive to Delphi, stopping in Corinth/Acrocorinth
Delphi for 2 nights
Athens for 3 nights
one night at Heathrow, on the way back.

We are assuming that each morning we will probably visit few sites within 30 to 90 minutes drive of where we are staying and then return to our accommodations in the afternoon.

Will take any recommendations for "not to miss" sites and attractions hear each.

We will Hit Nemea, and Micene, and Sparti, somewhere along the way.

If you have to X something, make it Sparta... even Greeks say, there is nothing there. Remember, Spartans were NOT into culture, or buildings, or art or beauty, they were all about fighting. So... no ruins of classical buildings, no gardens etc. Friends tell me that you wouldn't know this was an ancient capital at all, except for a few brass plaques and a couple of bronze modern statues.

A place in Pelops people don't realize has a thrilling background is Messene ... it has an amazing WALL That rivals some stretches of the Great Wall of China! The Messinians were held as "helots" (near-slaves) by the Spartans, and when they finally broke free, they wasted no time in building wall defenses https://en.wikipedia.org/wiki/Messene

Did this last summer with my 12 yo daughter (from Seattle :). She is way into mythology - it was such a memorable trip. Here are our favs/tips:

Our trip: Athens-> Nafplio-> Monvemvasia -> Mystras -> Zakynthos -> Meteora ->Delphi
Go as early as possible to avoid heat. It's less painful to get up early than be out in the heat mid-day.

Athens: see a concert at Odeon of Herodes Atticus. We paid to avoid crowds but there are also free concerts.
Nafplio: Mycenae was a favorite. Get up early to walk up Palamidi Castle. Be there when it opens so you can have the place mostly to yourselves. Then you will walk down the ~1000 stairs around 11:30ish am and see people sweating/stopping bc it's so hot.
Mystras: one of our favorites - the castle is incredible. It rained right before we got there so that probably affected our enjoyment for the better because it was much cooler (we were there June/July last year).
Zakynthos is super cool. I wanted an island/swimming (and did not want to get on a plane again as you mentioned in your post) in a secluded cove, which we found. Highly recommend Kanela Studios.
Delphi: totally worthwhile. Wish we had another day there.
Meteora: wanted to do the hike around the monasteries but it was too hot so we drove. Beautiful but probably fell a little flat as we visited the Grand Canyon the year before.

Fun part about driving in the Peloponnese was the goats! Once we had to stop the car to let a herd cross the road. Super easy to drive.

Just a suggestion about Athens. I just got back and it was my first time ever to Greece. The people are incredibly hospitable, friendly and helpful, on average, which was a wonderful surprise.
Athens is an edgy, busy city- motor scooters don’t stay on the roads, but jump up onto pedestrian walkways making for dangerous walk abouts- worse than Rome. The traffic on the main thoroughfares is mind- boggling and makes for a polluted breathing experience , but it’s quieter wandering around the Plaka as long as you keep your eyes on those scooters! To see the combo ticket package sights of the Acropolis and Ancient Agora you need at least 2 days and leave a day for the amazing Acropolis Museum. We also visited the Archaeological museum but that is at least another day to absorb the history.
Mythology is everywhere; you can’t visit Athens without feeling the real presence of Athena. I spent 9 days in the city, and it was enough- next time I’ll explore the Peloponnese and some of the islands. I like to live ‘local’ when I travel rather than hop from one spot to the next in too big a hurry. You’ll love the food!