Franny Rios mentions that the father of Eva's child has threatened to fight her for custody. Given that the child's father is in prison, his threat is not a realistic concern. Few judges would award custody of a child to an incarcerated parent when the other choice was the preserve that child's stability by keeping him with a relative who had been helping to raise him.
When discussing criminal records, Kathryn points out that Lucas had a record that included "B and E". (Breaking and Entering). The show is set in California - "B and E" is not a term that is used there, by cops or DA's, because there is no "breaking" requirement in California for burglary. A California Deputy DA or cop would simply say "burglary".