Why would the mother be tested to determine paternity? By definition, she’s not involved in that part of the equation.
What I understood was all three parties dna were needed to be conclusive.
To get a 99% certain outcome, the test will have to look at sites not on the sex chromosomes, so one needs the mother’s DNA to see which half of the child’s DNA to match to the potential fathers’.
That reminds me of the blonde joke about the blonde that was pregnant. But she wasn't sure it was hers.
Say mom has traits A-B,C-D, and E-F. Dad has traits U-V,W-X, and Y-Z. Child is B-U,D-W,and E-Z. Paternity is likely.
Child is B-L, D-M, and E-O? Paternity impossible. You know the traits that show up in the child came from neither the father or the mother (L, M and N). It is harder (but not at all impossible) to do it from just the father and the child. But it takes more work because you don't know if something the child has that the father doesn't didn't just come from the mother. But if after checking a few loci where the child has two traits, neither of which is present in the father........well you begin to establish that he is not the actual father.