So, since your question revolves around nuclear DNA and mitochondrial DNA let me start with this. Mitochondrial was once a microbe by itself and the theory is that, it could have been incorporated by phagocytosis into the eukaryotic cell and became a cell organelle eventually. The challenge in DNA evidence is that if you go with mitochondrial DNA, siblings will have the same DNA and it would be hard to identify who the actual person is or whom does the DNA belong to. It would also be identical to the mother. On the other hand, nuclear DNA being within the nucleus, it is highly unique to a person. Although, it does match to your parents since they are the people from whom you have received it. In a criminal investigation you always want to use nuclear DNA. When analyzing DNA at least in forensics, what the investigators look for are SNP. These are unique to a person and the chances of them matching to another person are way more than 1 in 8 billion. Thereby, it exceeds the overall population itself. SNP are single nucleotide polymorphisms, i.e., they are difference in a single nucleotide at that particular location in various people. Expert testimony becomes difficult when the case revolves around parent and children because their DNA is really identical, although SNP is very likely different. I hope this helps. :) Let me know if you need more help. It's kinda too much to answer.
