Complex sentence: The PR approach set the tone for poor relations between the McCanns and the "Polícia Judiciária", who were deeply suspicious of the way their investigation was being dominated, as they saw it, by British media handlers.
Split into simpler sentences: The PR approach set the tone for poor relations between the McCanns and the "Polícia Judiciária". This left the Portuguese police deeply suspicious of the way their investigation was being dominated, as they saw it, by British media handlers.