She noted that Austria’s agriculture minister, who hails from Nehammer’s center-right ÖVP party, had previously done exactly what she did: "Just a couple of weeks ago, [he] voted against my explicit will, for lowering environmental standards in [EU] agricultural policy."

Can someone who lives in a system with a parliamentary form of government -- which is nearly all of Europe -- explain how conflicts between ministers and prime ministers from coalitions are resolved? It's something that I really don't get.

In the US, the system is presidential. The President gets to make a call on executive policy. People can cut deals in choosing to support a candidate for president, but once he's in place, the President makes the call. There are some limited checks: departmental secretaries in the cabinet can resign rather than carry out an order, and the Senate must approve a President's nominations for a replacement. The President can dismiss a departmental secretary at will. And the President's formal directives, executive orders, are subject to judicial review, and the Supreme Court can decide that an executive order is unconstitutional. But in general, once a President is in the seat, he gets to make calls.

In parliamentary systems, control of the legislature determines control of the executive. In many electoral systems, it's uncommon for a single party to control the legislature, so it's necessary for a coalition to be formed to get control of the legislature. Those parties in coalition may have views that are significantly at odds with each other. One of the major things that is divvied up among the coalition parties are cabinet seats. Those seats control portions of the executive government. But someone becomes prime minister, and the prime minister is above all the cabinet ministers. And that prime minister is only going to belong to one of the coalition parties, usually the largest.

In parliamentary systems, there are definitely times when cabinet ministers -- who may not belong to the same party as the prime minister -- are not going to agree with the prime minister. In cases where that conflict exists, how is that resolved?

I assume that some degree of horse-trading happens at the coalition-forming time, at least for policy that can be determined at that point in time -- if Party A has a program that mandates that VAT rises 10% and Party B has a program that VAT is to be reduced 5%, I assume (perhaps incorrectly) that that is worked out at the time that the coalition is formed, and if it's impossible to come to agreement, then the coalition doesn't get formed, and the dispute between the cabinet minister and the prime minister doesn't come up.

But that can't catch all cases; not all policy decisions are going to be known at the time the coalition is being formed. Some are going to come up down the line. So for those:

Is this entirely up to the individual state, with mechanisms for resolution widely varying? Can a prime minister generally dismiss cabinet ministers? Can he generally annul their actions (as was apparently attempted here)? Who gets to decide on policy prior to the action? What happens if a cabinet minister is dismissed? Does the prime minister get to select a replacement, or the party who was granted the cabinet seat in coalition negotiations? What happens if a cabinet minister dies in office?