A pet peeve of mine is when people don't realize that a word can have more than one meaning. Especially when they are trying to make everyone else look like a horses a$$, (I thought it would be a good analogy with the horse racing theme).
Trifect from wikipedia is also stated as meaning.
The term has been extended to the realm of
politics, where it is used to describe a situation in which an executive of government appoints another elected official to a position and is also allowed to appoint his successor. This process can be chained together; in other words, the executive can appoint an elected official to a position, appoint another elected official to the other's previous position, and finally appoint anyone to the second official's position. The first permutation of this chain is called a "quadfecta".
The trifecta system is seen by many as a loophole in democracy, because it allows an executive to essentially override a choice by the voters. This is mitigated by the fact that the system requires the agreement of all parties involved. Executives have been able to get around this by making the position offered a very financially lucrative or long-term one.
Looking at this definition, one could definitely describe Parcells, Ireland, and Sparano losely as a trifecta. Especially since Parcells hired Ireland and Sparano for positions he once occupied. Albiet not by the Dolphins, but positions he still held.