Is Eric Flint’s Trail of Glory series (1812: The Rivers of War and 1824: The Arkansas War) in the Assiti Shards multiverse (a.k.a. 1632/Ring-of-Fire Universe)?
On one hand, neither of the three wiki pages linked above mention that it is (nor explicitly that it isn’t).
On the other hand, the similar book naming convention (as well as overall AltHist genre) hints that they might be, and I haven’t had a chance to read them to verify.
Goodreads suggests they are a separate series named "Trail of Glory".
From reading the entire set of both their certainly seems to be no connection. Nor is there anything in the Granville Gazette to suggest it.
Further consideration should be given to the technology available in the 1812 series which is not comparable to the tech in Granville 2 centuries earlier.
There's no way for them to be in the same universe, because Richelieu destroyed the English colonies in the Americas in 1633 (the year and the novel).
The alternate history of the colonization of North and South America as a result of the events in Europe unfolds in 1636: Seas of Fortune.
Completely scrambling the starting points of the map of colonial North America makes it impossible - both at the macro state level and at the level of individual personalities who wouldn't be born in our timeline until the 1700's - for the Rivers of War series to occur. That series requires the history of North America, Europe and the United States to be unchanged through 1811.
I would say no. All the Assiti shard stories are about the juxtaposition of societies from different times. There is no juxtaposition I can see in 1812, just straight alternate history. I haven't read 1824.
The only way I can see a connection is on the Uptime side. They might have both generated from the same home reality but I see no logical way the 1812 book could have leaped with no connection further up the timeline of the 1632 universe. No it had to have split off its own branch. Otherwise they would have in a totally random connection be more likely to appear in a totally unrecognizable world.
