Hi Jim,
"Where is my Native American ancestry?" and "Why is my Native American Ancestry not showing?" are among the most frequently asked questions
https://www.ancestry.com/corporate/blog/ask-ancestry-anne-where-is-my-native-american-dna/ and
https://www.youtube.com/watch?v=geE7zsehccYYour question has an element of this theme but you have pointed to evidence from mtDNA that might back up the family oral history. Autosomal DNA and mtDNA are very different tests and have a vastly different reach back in time.
mtDNA, as you probably know, travels back along the maternal maternal line virtually unchanged from one generation to the next. It is often used in archaeological and population studies. There are five main mtDNA haplogroups found in North and South American indigenous peoples; A, B, C, D and X
https://dna-explained.com/2017/03/02/new-native-american-mitochondrial-dna-haplogroups/ Autosomal DNA can be useful for family tree research back over 5 to 6 generations. Assuming a generation to be about 25 to 30 years this means one can trust autosomal DNA back to the middle of the 19th century. However ethnicity estimates are merely comparisons of your DNA with a reference panel of geographically diverse modern peoples. Each direct to consumer DNA testing company uses different reference panels and testing algorithms. Testing with each of the main four DNA testing companies will probably give you four different results. These ethnicity estimates are often amended as new data is added to the reference panels and as algorithms are updated.
The next issue with autosomal DNA is that you see dilution with every generation. You inherit 50% of your DNA from each parent and about 25% from each grandparent. By the time you get to your great great grandparent you are only inheriting about 6.25%. As you go further back you will not see every ancestor represented in your genetic makeup because of random recombination of the chromosomes.
So if your wife's great great grandmother was 100% Native American, for example, then your wife might expect to see about 6% Native American in her ethnicity estimate, assuming that the DNA testing company had a representative reference panel. However, if the great great grandmother was herself only 25% Native American then your wife might only expect about 1.5% Native American. Or indeed she might see 0%. It is not an exact science. Indeed some people argue its not even a science!!
The references from Ancestry and Roberta Estes above have some useful information. Why don't you take the mtDNA at Family Tree DNA and see if it falls into one of the five main Native American haplogroups. That is more likely to provide confirmation of your family oral history. FT-DNA have regular holiday sales and may have offers to coincide with the RootsTech 2022 conference (3-5th March 2022).
pughcd