I was asked to define politics in the briefest of terms. I said that politics was "who gets what". A discussion ensued, but no clear resolution. Am I more or less accurate in my view of what politics is?
You are pretty far off the mark there. Politics is basically the actions related to the governance of an organization, doesn't need to be government at all, and defined by the different sides involved in the debate with different views. A good non-governmental example would be a union negotiating with corporate for higher wages, that is the simplest way to look at the definition of politics. The actual result is irrelevant, politics describes the process to get to that point.
Politics determines who controls the money/resources, who makes the laws, which lives are considered valuable and which ones are not. Politics also determines who writes the history books, and what is included and what is left out of those books.
I fully explained what politics are, not sure what part you are not understanding. To more generalize it you can define politics as two sides engaging in actions to affect the outcome of a situation. This could even be applied to the family unit although that is not really what the word was developed for.