you can get the swim shoes at all the local markets in the towns and vilalges along the coast. Plus all the cheap beach stuff type shops and the shoe shops (of which there are a lot) and in places like emmezetta (italian owned department store) or the children's shops such as the Turbo Limac chain. i.e. there is no problem getting them in Croatia at all! Prices are about 30kn - 50 kn (i.e. £3 - £5).
Children's food is easy to get.
Water is good in September.
Beaches are pebbles mainly because local council dumps fresh pebbles on each beach in late spring.
The parents were probably at the Plitvice Lakes. If you are in mid or north dalmatia, then Plitvice is a long way to go with young children but Krka Waterfalls also make a good day out.
I'd hire a car if I were you: its the only decent way to get about. Croatia is really a place for wandering around old towns, and relaxing on the beach although it has great sailing too and there are a lot of yachts around, especially in August.
Ice creams are good and cheap (50p) as is pizza (£4 in a restaurant). Pasta is everywhere, and steak and chips (called "pommes frites") but sometimes the tourist food is otherwise a bit limited. The water is drinkable (Croats think it is UK tap water that should be boiled!).
Everyone under 30 speaks english and most educated over 30s do too, so communication should not be an issue in the resort areas.
Be wary of going to dubrovnik with young children. its a great place to visit but since the cruise ships started going there it has become so mobbed, it can be difficult to see anything. If you are in mid-dalmatia, then Hvar town is a must!