What are my accommodation options when traveling with toddlers through Morocco?

Skip Agadir, unless you are extremely exited about tourist traps.

Marrakech is very nice, as is Essaouira, although the two are not comparable; Marrakech is a proper city with an old historic city centre, cluster with souks (=markets); Essaouira is a laid back town at the coast, it also has an historic centre, but is much smaller.

Accommodation is generally easy to find. There usually are plenty of places to sleep and/or eat, although it can get pretty busy in the high-season.
As far as I know, a 'Riad' is what we would call 'inn' or 'guesthouse' i.e. a place for travellers to sleep. I know some nice and luxurious places call themselves a Riad, but I've also stayed at some very-low-budget (€ 3,- per peson/night) accomodations that where called a Riad; those accommodations where not aimed at tourists but at moroccans.

The other options you have greatly depend on the amount of time you plan to spend in the country as well as what you like to do; visit cities, explore caves, climb mountains, visit the (edge of the) Sahara, go see the 7th largest mosque on earth, go surfing in Dakhla or relax on the beach in Rabbat.

Riads are traditional Moroccan houses, not more than a couple of storeys tall and built of bricks / mud bricks. Due to the architecture, it's like staying in an olden-day house when people used to have multiple families living in one house. This experience is definitely suggested. Most riads except for the really cheap ones are quite comfortable, have 'Western-style' flush toilets et al. So in that sense, riads in Morocco are like B&Bs anywhere else. What many of them do lack is any kind of heating / air conditioning; the structure and the materials the house is built with itself is supposed to help regulate temperature.

Given the exchange rate, you may even find it quite cheap to stay in budget hotels and get a slightly more comfortable stay without breaking the bank. I would say, in Marrakech, stay in a hotel and in Essaouira, stay in a riad. Essaouira is a really small town and there's not much to see so I'm guessing you won't be stopping there for long, so if you decide to stay in hotels elsewhere than you can at least have the experience of staying in a riad at one place.

Riads will be quite expensive if you are traveling with kids. Nice ones can easily be 80-100 euros and that normally only gets you one bed so you would probably need two rooms. They also tend to have a very small number of rooms so your two rooms may not be next to each other or even on the same floor. Given that, every riad is different so you may certainly find one that has a suite-style room that could accommodate your whole family. Booking riads is quite an endeavor since there are dozens of them and each is very small, so I suggest you don't get your heart set on a particular one since they are often booked up when you try to reserve.

The other option besides a riad is a standard western hotel. These will be outside of the old towns in the new city, so less character and you will need to take a (cheap) taxi to get anywhere. Often there will be a Hotel Ibis right next to the train station. These are reasonably priced but don't include breakfast and the rooms are small and charmless.

(Personally, even as a young couple, we got a bit sick of riads and ended up staying a few nights in a hotel to get a comfortable bed and a decent bathroom with a good shower.)

We are currently travelling through Morocco with our kids. It is really a very good choice to go with young children. On the downside, we learned that one thing NOT to do while traveling with kids, is to stay in a Riad. How romantic and beautiful they might look, the internal square makes your stay an accoustic nightmare. Not only for you, but also for your fellow travelers.

After two nights of constantly trying anything to keep the kids quiet we came across a brilliant kasbah, close to the Ouzoud falls, who had berber tents. From there on we just asked the owner for recommendations on similar settings around our next destinations. Works like a charme. Both the kids and the parents are enjoying the vacation to the fullest