Melanie, I don't want to rain on your parade ... but cooking/food prep experiences of only half a day are VERY hard to come by, and even more so off season, as you will be. Many many of these are essentially full day experiences (starting 10 am - then lunch on the results around 2 ), and often are just for whole busloads of people, arranged in advance. Even for a privately-arranged thing, I doubt whether that cheesemaking - shepherd thing of your link would be available at your timing.
However, that is a wonderful site for family experiences, one tour could be be arranged even off-season because it's right IN Rethymnon. It's the gourmet family food tour -- https://www.kidslovegreece.com/en/activity/family-food-tour-rethymno-gourmet/ ... does visit retail shops instead of a farm, but many have their OWN farm supply, and certainly can talk at length about how they make THEIR special yogurt or prepare THEIR own special olives (greeks looove to talk about this).
However, I now realize, re-reading your paragraph that Crete is not on your list... not worth going there just for food tour! In Athens there are a lot of cooking classes ... but I don't know if kids would enjoy so much. However, you ARE going to one of the most fertile agricultural areas in Greece the valley of the Argolid .. and here's a link where you can inquire about such things as visit where they produce olive oil... and also mentions "culinary tours" http://www.ecotourism-greece.com/tourism/activity/eating-drinking-greece/argolida -- It suggests visit to cheese-maker, orange groves etc. Do NOT miss fresh Orange juice in Argolid!! NOTE: several of these places are on the way to EPIDAURUS; u can e-mail ahead, contact info on website.
You don't say what age your kids are, but on your destination list, there are 3 dont-miss experiences I recommend that really will enrich their experience:
ATHENS - Cycladic Art Museum (under 12 free). Top floor has WONDERFUL video, w. young greeks of today, in costume, showing the experience & customs of ancient Greek Youth ... really makes the culture & beliefs vivid for children.
ATHENS - Acropolis Museum. The top floor also has SUPERB 20-minute video - photos AND animation that makes the whole history of Acropolis and Parthenon exciting & understandable for kids. I've seen kids totally mesmerized at this showing.
NAFPLIO - Wonderful museum right on the marble-paved square, 2nd floor of historic armory ... can be seen in v. short visit. At the entry, do NOT miss another terrif video -- in 15+ minutes makes the ancient history of area enthralling & real, and prepares them to realize the awesomeness of several exhibits (the world's ONLY existing Iliad-era suit of armor... thrill thrill).
NEMEA -- Enroute to NAFPLIO -- if u are driving, it's right on the way!!! On the big highway, where the exit SOUTH goes to Nafplio, the exit NORTH just before, only 5 mi off the highway, is this super "runner-up" to Olympia as sacred games site. Only takes u about 60-90 minutes see the whole thing, but there are huge temple columns. ruins and stunning stadium where kids can race from starting blocks 2300 years old! Every 4 years today, runners from all over world come here - http://nemeangames.org - this website shows the excitement. BTW -- after you visit Ancient Nemea, about 5 minutes away is the village of Nemea. Right on the main street is a bottling-plant for Nemean Red Wine. (it has a Huuuge Tank in back yard, can't miss it!). You can see bottles going around an assemblyline getting labels. Also, in Ancient Nemea Museum, the staff knows ALL about the area, and you could ask them if there's a farm opportunity around ... orange harvest, grape harvest right when u will be there.