Skipping Chefchouen, does not seem worth it. Here is my current itinerary:

Fly in to Marrakesh (afternoon), stay for 4 nights (day trip to Atlas mountains and)
Go to El Jadida (2.5 hours), stay the night there
Train to Casablanca, then on to Fes, stay for 3 nights (day trip to Moulay Idriss)
Train from Fes to Casablanca, stay 1 night in Casablanca
Fly back home from Casablanca (afternoon)

Is El Jadida worth the detour for some relaxing time on the coast, away from touristy Essaouira? Or we could head straight to Fes and spend more time there. Is it worth spending more time in Fes than Marrakesh? We are not interested in shopping, and more interested in culture, food, architecture, and of course entertaining the kids. Is there a good suggestion (easy to get to) from either Marrakesh or Fes to take the kids for a camel ride (less touristy the better)? Alternatively we could spend 4 nights in Marrakesh, fly to Fes, spend 4 nights in Fes, train to Casablanca, 1 night there, and then fly out of the country next day.

Agree with Michel, you cannot do desert trip, or you can do it, but then no Essaouira, only Marrakech a couple of days and the desert. And fly out from Fes where you can stay a couple of nights also.

..... it would be helpful to know where you arrive and depart Morocco, dates and time.?

Arriving at Merzouga and arranging a trip into the Sand Dunes in Mergouga is a good idea, in September the weather can reach the high 40's. almost 50cc. at times, waiting until at last moment to pay for/ book a trip keeps you in control whether to go into the Desert or not. On arrival find a hotel, rest and settle-in, enquire at reception for up-to-date information about tours and the crews/companies...... or find one the many tour-agent offices etc. around town, you might meet returning fellow tourists to ask of their experience, be cautious of pushy touts looking for victims lurking around buses or hotels. You also have an opportunity to see the vehicles. crews etc.
Tour groups may be a process of consolidation of singles, couples or small numbers of tourists to make-up a viable group, without consideration to compatibility of fitness, age or interests.! Small private tours are expensive.

Inter-city buses vary widely on issues of standards, comfort and facilities. ONCF/Supratours Bus is probability the best standard bus between Marrakech and Merzouga, there are mandatory stops for toilet-breaks and snacks en-route.

Links for inter-city and taxis buses in Morocco:-

http://www.oncf.ma/

http://www.ctm.ma/

https://www.lagare.ma/en/city/city.php

http://reversehomesickness.com/africa/taxi-fares-morocco/

Marrakech City-Bus including the No.19 Airport Bus... http://www.alsa.ma/fr/marrakech/itineraire-urbain

...... to make a few comments and suggestions.

If the trip to the Sand Dunes in the south are a priority, with the short time you have travelling as a group of four, the proposed itinerary is too much for the time. The advantage of four, the economics hiring a car makes sense, the logistics of moving four, all being ready at the same time, the necessary and various stops/breaks is more easily managed.

So drop Fez and shorten the overall road trip. Travel by train from the Airport to Marrakech, enjoy your time there and recover from the trans-Atlantic flight.
Then hire a car, I recommend the shorter trip to M'hamid via Zagora and Ouarzazate rather than Merzouga, it's a smaller area of sand dunes not that you'll notice anyway, importantly, a shorter road trip with fewer tourists.
Research and compile an itinerary for this trip, and return to Marrakech, return the car in advance of taking the train back to Casablanca.

At the Airport there's a Railway station in the basement, with one stop/change of train at either Oasis or Casa Voyageurs, ask when buying your tickets which station to change at.....
http://www.youtube.com/watch?v=W4guUsiphhA

For Marrakech I recommend you get the Lonelyplanet City Guide to Marrakesh recently up-dated, well worth the money, might save you a multiple the cost of the guide. Jardin Majorell in Gueliz not to be missed, City-bus ALSA have some long route routes into the countryside, the mountain village Amizimiz south of the City on the No. 41, or the Hamada Desert Agfay on the No.33.....
http://alsa.ma/fr/marrakech/itineraire-per-urbain
http://alsa.ma/fr/marrakech

Have you chosen a hotel for Marrakech yet.?

Adding to the itinerary for our group of four. Enter Morocco at Tangier and using a private car for travel to Chefchauoen, Fes, followed by Marrakesh, over to Quarzazate, back to Agadir and depart Morocco. Thanks for your input.

Landscape: The Annapurna Circuit let's you walk (or ride) through subtropical jungle, up into high alpine areas and then down into a real desert, while the EBC Trek has even better mountain scenery but then only two to three days in forrests and all the rest is high alpine scenery.
Similar with culture: In the beginning and the end of the AC you will visit areas where various different "tribes" (not sure if that's politically correct - sorry if not) live while in the Khumbu you'll mainly find Sharpas and culturally similar "tribes".
Both have excellent lodges. Both will be similarly crowded. Both can be done without a guide, both will cost you about 50 dollars in permits and then about 30 dollars average per day for food and lodging (maybe EBC a LITTLE BIT more).
However EBC will require you to pay about 250 to 300 dollar for flights, or you start with a jeep ride to Bupsa, which takes 1,5 to get there vs. 6 to 7 hours to get to Besisahar, the AC trailhead.
The AC has a road running alongside most of it, complete with buses, Jeeps, cars, tractors, trucks and motorbikes, which makes the crowd of tourists you meet there very different to the crowd of tourists you might meet on other traks in Nepal. On my trek a few month ago i realized that a large portion of visitors chooses to go all the way up to Manang in Jeeps and doesn't actually want to engage in any sporty activity like trekking. There were even groups that traveled to Manang by jeep and then continued on all the way to Muktinath on mules, crossing the pass riding. All were altitude sick and it was a very pitiful sight.
The roads on the one side up to Manang and on the other side down the Kali Ghandaki valley can be avoided in parts using the so called NATT trails established in the early 2010s, however some of them are meanwhile also replaced by smaller dirt roads. Last fall we walked from Dharapani to Muktinath, and the first 2 days were almost entirely on the dusty, smelly, load, annoying and sad road. From Dikur Pokhari it gets better. The road bit between Muktinath and Jomsom is now even blacktopped. In the Kalo Gandaki Gorge a large part of the road can be avoided, but also not all of it. We saw several poor trekkers making there way through the dusstorms the jeeps created.
In the Khumbu there is no road. Period.
If you want to know about other aspects of the treks, please ask.
By the way, the best trek in the Khumbu region in my opinion is Gokyo, because of Gokyo valley being much prettier than the valley EBC is in. The view of Everest from Gokyo Ri is at least as good as the view from Kala Pathar. Again - in my opinion.