Your 1851 Colt is the large round trigger guard variation in (from your description and what I can see in the pics) NRA Fair condition should be worth about $2200, give or take a few bucks.
You're right about the oral history of the revolver. About all you might be able to verify is that Your Uncle's Great-Grandfather owned it. A collector will value the gun based on model and condition, not supposed history. The rule is, you buy the gun, not the story. What's neat is that the Colt has been in the family for nearly 150 years and I applaud your intention to keep it that way!
I think of my gun as a tool for converting worthless human garbage into valuable fertilizer.