Hi, Mel. Mitochondrial DNA is excellent for disproving an hypothesized relationship, but not very useful for matching or forming an assumption of an exact relationship. The reason is that the tiny mitochondrion--we typically have over 100 of the organelles inside each of our cells (except red blood cells)--contains a grand total of only 16,569 base pairs in its DNA molecule. As DNA goes, the whole thing isn't even large enough to register as a single segment if we were to plop in down onto one of our human chromosomes and look for it with our current direct-to-consumer autosomal DNA testing technology.
Accounting for over 80% of those base pairs is a regulatory region and 37 genes. Mutation can't mess much with those areas without being potentially disastrous to the host human cells. So only a little over 3,000 base pairs can safely mutate to provide us differences in our mtDNA.
There simply isn't enough possible variability in the tiny mitochondrial DNA molecule to differentiate to any granular level among different individuals for purposes of genealogical matching. There are about 7.6 billion people alive right now, and they all share very similar mitochondria with relatively few differences. In other words, a whole lot of people will share the exact same mtDNA as your mom. In fact, haplogroup H is by far the most common in Europe, and the H3 clade is second only to H1 in frequency.
If two people don't match, it's confirmation that they do not share a maternal ancestor. A match, even at the full-sequence level (what's called the "coding region") means you do share a common female ancestor, but there really is no way to determine with any exactitude when that ancestor lived. In its general matching guidelines, Family Tree DNA states that an exact match (genetic distance zero) of the full-sequence test represents a 50/50 chance that the common ancestor lived within the last five generations, or about 125 years. To reach a 95% confidence level, that timeframe increases to 22 generations, or about 550 years.
While mtDNA mutates seldom and slowly, compounding the problem with using it for genealogical matching is that all its mutations are heteroplasmic. I'll spare you the biology :-) but suffice to say that you and your mother might be a genetic distance of one from each other, but her ancestors might be a genetic distance of zero from her for the past 2,000 years. That's one reason that mtDNA isn't entirely suited to triangulation like yDNA is; the Y contains over 59 million base pairs, and the vast majority of it is "junk DNA," free to mutate (it has only twice as many protein-coding genes as mtDNA despite being over 3,500 times larger), and it isn't heteroplasmic.
It sounds like you have a good hypothesis to chase, but mtDNA may never be able to serve as verification of close biological relationship to the Whitfields. Even with a perfect full-sequence mtDNA match, the most recent common ancestor may have lived in the 1300s.
