Formidable sentence. 法案通過 is a compound: 法案 (bill) + 通過 (passage). 推進する ('to promote, push forward'). まぎれこませる is a causative of まぎれこむ ('to slip in among, become mixed in'), so the overall verb means 'to cause (the bribe money) to slip in'. The formal tone fits the political/journalistic subject.