As for why Maxwell stayed in the US, who knows?
If she’d headed off abroad in the face of an active investigation, she would be returned via extradition at some point, then potentially classed as a flight risk and incarcerated rather than allowed out under house arrest.
Being in the states allows her to consult with her legal team, and negotiate with the federal authorities, again building a picture of cooperation which might keep her out of a cell.
If she does have significant dirt on someone powerful, the US (outside prison) is a lot safer place to be than pretty much any country, including the UK, as she would be under surveillance by the authorities.