I can relate to catching people (both at work and family members), having done something wrong (I have witnesses) and they never admit they erred (continue to lie about it). What is hard about when it is a family member is that because you love them, you believe their lies for a long while causing cognitive dissonance (you think you are going crazy) until the proof becomes obvious....

Once you are no longer fooled, you can practice better boundaries. While, if they respect your boundaries, it is a very good thing to forgive them but a part of you knows that you have to be careful not to be a fool again.