In Britain, Lady Louise attends St George's School in Windsor Castle. I imagine that Viscount Severn will also attend. Her second cousin, Margarita Armstrong-Jones, attends Garden House in Kensington. If I'm correct, Margarita is of the age where children leave primary school, so she probably doesn't attend any more. I've read that Lady Sarah Chatto's sons, Samuel and Arthur, are attending Eton College in Berkshire, although I'm not sure if that's accurate. St George's and Garden House are both private/preparatory schools. In the UK, most people call Eton College a public school (in England, public schools are schools that are usually one of the top schools in the country. Most of the public schools are fairly well known and pupils usually board there).
In Belgium, (I've read that) Princess Louise, Prince Nicolas and Prince Aymeric attend the Lycee Francais de Bruxelles, a French school in Brussels. I also remember reading that Princess Astrid's daughters used to attend Sevenoaks School in Kent. I think the Lycee Francais de Bruxelles is a public school, although I'm not sure. Sevenoaks is a private/public boarding school.
I would imagine that the Behn sisters attend school in London since they live there.