Secession was never seriously discussed during the Hartford Convention. There were those there that promoted it, true. But they were a small minority and never came close to having their proposals made part of the convention final report.
That is totally false. The Hartford Convention was assembled for the explicit purpose of seceding from the union. The only reason that did not come about is that the war ended a few days before the convention started. They instead drew up constitutional amendments restricting the federal government's ability to make war and to regulate trade. The convention's delegation to Congress was recognized and scheduled to present their amendments to Congress when news came of Jackson's victory at New Orleans. Public opinion turned sharply against the Hartford delegation. Their presentation to Congress was cancelled, and they left Washington with the French embassy staff lining the road hooting them out of town.
The Hartford Convention was a serious affair and nearly led to the breakup of the United States. The only thing that prevented this outcome was the timing of current events. Had the war lasted another month, or had Jackson not defeated the British so decisively at New Orleans, we probably would have ended up with the United States of New England.
Here are the proposed amendments. Note the last resolution. It basically says adopt these amendments or we're going to secede.
Amendments to the Constitution Proposed by the Hartford Convention : 1814