Media sympathy for the family in the UK could also evaporate rapidly if there look to be serious implications for UK/US relations.
Actually I don't think it will. In an awful way it's the perfect David v Goliath story. Young, white English, completely innocent kid, loving and articulate family who are grieving but not vengeful, killed by someone with a dodgy driving history travelling on the wrong side of the road, who promptly lied to the police and buggered off out of the country when she might not even have diplomatic immunity anyway.
While in the past the tabloids have been able to obfuscate the central facts of huge cock-ups via a bit of victim blaming (cf Jean Charles de Menezes) there's no wriggle room for them here, and the family aren't going away.