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?
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.
1. Mitochondrial DNA is less apt than regular DNA to accurately identify motherhood since it has a low mutation rate.
2. The mitochondria would still come from the chimeric cells which still are a generation away from the mother's cells.
3. If you have have considered the possibility of chimerism, there are much simpler tests - e.g. the tests that they did do.