Beth,
I don't know what part of Arkansas the diamonds are in. But, I'm sure the age of the deposit is known. While I don't know the age, I'd guess it was in the hundreds of millions of years old. So, I suspect that your 1811-1812 hypothesis will not fly. You can probably spend some time on Google and find the age.

As to link with Hot Springs, I don't think that is easy to check. They are not close together. I spent a few minutes the other day checking a town with "springs" in its name between Hot Springs and the quakes, but did not find the nature of the springs. Southern Missouro Ozarks are full of giant springs that are just caves coming to the surface; are nothing deep-seated.

I have no idea why Hot Springs Arkansas is hot.

Chris