There’s only 2 reasons for them to live abroad in a country that they don’t want to:
- Money: Switzerland is a relative tax haven with low tax rates and is renowned for its secrecy when it comes to banking there. Obviously they want to stay out of the UK to avoid pay tax to HMRC and I highly doubt that them leaving the US was anything to do with schools- they probably just didn’t like the IRS getting to have a full look at their finances.
- Custody: Staying abroad ensures that James Stunt can have no access to the kids. He isn’t currently allowed to leave the UK.