Could I isolate just my fathers DNA filtering out all mitochondrial (maternal) DNA?
Mitochondrial DNA is maternal. This does not mean all the maternal DNA is in the mitochondria. You can actually pretty easily separate mitochondria from nuclei. The mitochondria will contain maternal DNA, and the nucleus will contain 50/50 from both parents. You could separate DNA by sequencing it, and both your parents to determine which gene came from which parent, but that’s difficult and expensive. The Y chromosome is the only piece of DNA that is identifiable as paternal based with any simple experiment, and obviously that is only useful if one is themselves male.