Teacher here! The options to consider really depend on your child, but here are the things that spring to my mind:
Have you considered a boarding school in America? This would depend on how long you move over for. Is it likely to be more than two years? What are your child's post high school ambitions? University? In America or flexible? UK universities have really specific courses that you apply for on application (like choosing a major when you apply).
I work at a boarding school with a significant number of foreign pupils. Some enter A Levels having done a year of GCSE study (normally they have taken a reduced number of GCSEs, say 6 or 7) in order to enter A Levels. This means many of my A Level pupils from abroad are a year older than the English kids I teach. I also reckon it all may depend on what three (max four) A Levels your daughter might want to take. For example, there are a large number of social science A Levels not offered at GCSE so a school might be a bit looser with their requirements for entry.
IB. Not sure any state schools offer IB though...
Have a quick google, it looks like the closest schools to Durham would be:
Durham Gilesgate Sports College and Sixth Form Centre - Bradford Crescent, Durham City, County Durham
Newcastle Sixth Form College - Newcastle College, Parsons Building, Rye Hill, Scotswood Road, Newcastle upon Tyne
South Tyneside College - St George’s Avenue, South Shields, Tyne & Wear
St Robert of Newminster Roman Catholic School - Biddick Lane, Washington, Sunderland, Tyne and Wear
Tyne Metropolitan College - Embleton Avenue, Wallsend, Tyne & Wear
There are probably additional IB options if you start to look at boarding, some of which would be not tooooo much further away, but definitely not commutable daily.