[josu]

AFAIK -and please do correct me if I am wrong - twins have the same mitochondrial DNA, therefore even if she is a chimera all her cells should share the same mitochondrial DNA.

And isn't testing for mitochondrial DNA fairly simple/cheap?

[ronaldx]

Mitochondrial DNA between twins is expected to be almost identical, but you and I also have extremely similar mitochondria: since it doesn't recombine and rarely mutates. So, you have to get to a much deeper level to identify the differences.

Even if it's now possible/cheap, that's a recent development.

mtDNA is good for finding your (maternal) ancestral group, less so for your immediate relatives.