I guess that depends a lot on each country's political structure and conventions. In Germany the Bundeskanzler (the chancellor is the equivalent of a prime minister) has the final say. This principle is called Richtlinienkompetenz (directive competence). He or she can basically order members of his cabinet what to do. It has been used only twice since 1949, because it is a harsh instrument which always threatens to end a coalition resulting in the election of a new chancellor or even a full election. On the other hand it allows the coalition party who is against the decision to show it is not willing to give up this position other than by force. This can save a coalition because it allows the government to continue its work even if a decision is necessary that would otherwise result in a breakup of the partnership. In almost all cases these situations are therefore solved by negotiations between the coalition partners.