Reins (no G in it) are what you control a horse with, and by analogy they're used to indicate such control (as in the idiom you mis-used); it comes from Vulgar Latin "RETINA", constraint, from "RETINERE", to constrain (from "re-tinere", literally "to hold again"); close cognates in English include "retain" and "retinue".
A reign (with a G) is the period during which a certain monarch is on the throne, that monarch's authority and dominion, his or her rule; it comes from Latin "REGNUM", kingdom or reign, related to "REGULARE", ``to rule''; deep down, it coms from Proto-Indo-European root *reg-, just like your own surname, and a wide variety of words such as "right", "rich", "Raja", "rector", "erect", "royal", "realm", "rule", ... which got into English through many different routes.
It IS unfortunate that these unrelated words, rein and reign, ended up in English with the same pronunciation, very similar spelling, and even vaguely cognate meanings...!-). But PLEASE think of their differences, and let your readers focus on the very important and relevant messages you're sending (in this latest blog, about the horrors of the GSEs, Fanny and Freddie, based on private profits but socialized losses), rather than risk apoplexy over your usage of English... THANKS!