Vehemently is how you do something when strong feeling is pushing it out — you say it forcefully, and you will not be talked out of it. It attaches to verbs of speaking and opposing above all: deny vehemently, vehemently oppose, vehemently disagree, argue vehemently, vehemently reject. In fact 'vehemently deny' is so common that it has become the standard phrase in news reporting whenever someone is accused of something: 'He vehemently denies the allegations.' There is a quiet irony in that phrase — reporters use it to show the person is pushing back hard, while carefully not saying whether the denial is true. It is formal and mostly written; in speech people say 'strongly' or 'flatly denied it'. Word order: it sits before the main verb ('she vehemently opposed it') or after it ('she opposed it vehemently'), and either is fine.