How should we handle this woman our father is involved with?

This is a control thing for her, and the best way to bring down a control freak, is to keep calm. If you confront her in front of your dad, it will only further her attempts to make you and your family seem out of control. As hard as it will be, you can't play her game. Just be a loving daughter and ignore the Sh*t out of his wife. It will poke holes in her lies.