Yes that's correct, if you are getting the free half board offer you only get a counter service breakfast in the park. You get a hot drink, a juice and a choice of 2 items (pain au chocolat, croissant, bread roll, bacon omlette burger). If you want to have a hotel breakfast you have to pay extra each morning, and that's only if they have availability, it's not guaranteed.
I know it's awkward for people who have special dietary requirements, I'm a type 1 diabetic so a carb heavy park breakfast isn't great for me either but there are soooo many people with various dietary/health needs that they can't make exceptions because they'd be making hundreds of exceptions every week. My eldest son is also autistic but he will eat pain au chocolate and croissants with jam so he should be okay. Maybe you could take some breakfast cereal bars or something with you that your children will eat?