Here are the results of my own research on the subject of areas of the USA which were colonized by the three major North American colonial powers.
Various groups of Amerindians (Indians or Native Americas) once ruled or at least lived in every region in the lower 48 states in the USA.
As far as I know even Aztec legends never indicated their ancestors ever lived north of the Rio Grande, so I am ignoring the Aztecs.
In 1873 General Crook's proclamation of victory over the Tontos said that his troops had ended a war which had been going on since the time of Cortez, apparently implying a connection between the Aztecs and the Apaches. If an official document could exaggerate that much, Morticia could exaggerate equally much in an offhand statement, and I don't think we need accept a period of Aztec rule.
[added oct. 8 2023. Possibly there was some sort of Pre Columbian Mesoamerican rule of part of what later became the USA and Morticia referred to those Mesoamericans as "Aztecs". Perhaps the book happens in the same fictional universe as the 1963 movie Kings of the Sun.]
Great Britain ruled the 13 original colonies along the Atlantic coast and also granted to the new USA in 1783 the lands east of the Mississippi River and south of the Great Lakes it had acquired from France in 1763. Great Britain ruled Florida (including southern Alabama & Mississippi) from 1763-1783.
West of the Mississippi Great Britain ruled or claimed parts of Minnesota & North Dakota until ceding them to the USA in 1818. Great Britain and the USA shared rule of the Oregon country from 1818 to 1846, when Great Britain got the northern part and the USA got Washington, Oregon, Idaho, and parts of Montana and Wyoming.
France claimed the Mississippi River basin, or about half of the lower 48 states, though their forts and settlements were thinly spread. The part east of the Mississippi were ceded to Great Britain in 1763 and became part of the USA in 1783. The part west of the Mississippi was ceded to Spain in 1763, back to France in 1800, and then to the USA in 1803.
Spain originally claimed to rule all of the Americas west of eastern Brazil.
A Small French colony was established at Charles Fort on Parris Island, South Carolina in 1562 which was abandoned in 1563. A second French settlement there lasted from 1577-1578. The Spanish settlement of Santa Elena on the same site was occupied from 1566 to 1576 and from 1577-1587, the region was later ruled by Britain for about a century before the American Revolution.
But Gomez implied that the USA acquired the region they lived in from the Spanish government.
In 1819 a border treaty caused Spain to cede a small part of Colorado to the USA; there were probably never any Spanish, French, or British settlements or forts in that area. Spain also ceded the western part of the state of Louisiana, which probably had a few French and Spanish settlements and forts. I don't think that the British ever had settlements in that part of Louisiana.
Spain ceded East Florida to the USA in 1819. A French settlement was at Fort Caroline in modern Jacksonville from 1864 to 1865. The Spanish established Saint Augustine in 1565. And East Florida was ruled by Spain from 1565 to 1763, by Britain from 1763 to 1783, and then by Spain until 1819.
Spain also ceded West Florida to the USA in 1819 (which had been occupied by the USA since 1812), a region including the southern parts of Alabama and Mississippi and eastern Louisiana. The French established Mobile, Alabama in 1702 and Biloxi, Mississippi in 1720. The region was ruled by Great Britain 1763-1783 and then by Spain until the USA acquired it.
Natchez, Mississippi was founded by the French in 1719. The region was ceded to Britain in 1763. During the American Revolution, the Spanish captured the region in 1779. It was ceded by Britain to the USA in 1783, but Spain retained it until a US military expedition claimed it in 1797.
[added Oct. 8, 2023. So I guess that the most probable locations for the Addams family in the Addams Family (1965) by Jack Sharkey, 1965, should be in the area around Parris Island, South Carolina, or the area around Jacksonville and Saint Augustine, Florida, or the area around Pensacola, Florida and Mobile, Alabama, or the area around Natchez, Mississippi. And the last three areas seem more probable because the USA acquired them directly from Spain.]
[added 10-09-2023. That same chapter says that Uncle Fester served in the Continental Army during the Revolutionary War. That might indicate Fester came from one of the 13 colonies, but he might have been a more or less foreign volunteer like Lafayette, von Steuben, Pulaski, etc.]
I am rather surprised that there are any regions in the USA which have been ruled by Spain, France, and Britain, and I suspect that Jack Sharkey would have been equally surprised to learn that there were places which had been ruled by everyone he mentioned (except the Aztecs).
Most of those regions were were ruled or settled or claim by Britain much longer than by France or Spain (South Carolina) or by Spain much longer than by Britain or France (East Florida), or by France much longer than by Spain or Britain (Alabama & Mississippi).
And I would certainly be pleased if someone pointed out a region where the three colonial powers ruled for time spans closer to being equal.