Why was there a covenant cut with the benei Yisra'el at Sinai, then at Chorev, and yet again at Mo'av?
It would seem there are two covenants established between the Bnei Yisroel and Hashem.
The first was at Sinai or Chorev. Chorev is another name for Sinai (See Rashi 3:1)
This covenant constitutes the "ספר הברית" that commits the nation of Israel to keep all the commandments that are commanded to them. (See Ramban Exodus 24:1 for a timeline and description)
The Covenant at Moav seemed to be an additional covenant between God and the nation of Israel. This covenant encompassed the providential relationship between God and the nation. In this covenant the consequences to the nation of adherence to the "ספר הברית" are outlined. (See Ramban 29:1)
The Rashbam says Chorev is a reference to the consequences outlined in Parshat Bechukotai רשב"ם על דברים פרק כח פסוק סט (סט) בחורב - תוכחו' שבפרשת אם בחקותי שכתוב בסופן ביד משה בהר סיני. הוא הר חורב:
There seems to be debate as to the exact objective of the Bris at Moav.
See Rabienu Bachya, Ababrbanel, Rav Hirch all have perspectives on it.