Mitochondrial haplogroups tend to be very old and not of much use for showing a positive relationship, though if two people test and have DIFFERENT mt haplogroups (and one not just being a subclade of the other) then you can rule out that the mother's mother's mother's etc. are from the same mother.
If both of you can show a pedigree back to the same woman, through the single path of only women in your pedigree, you ought to have the same mitochondria. But, you both would need to do a full sequence ($199 at FT DNA) to make sure they are identical.
You mentioned you had an uncle - if he is still with us then testing him would be the best bet to gauge how close the relationship is to this match.