I'm confused, hurt, and anxious.

How do I confront my father about his infidelity? Honestly, my mother and I don't care much anymore as long as we're provided for. The real problem is the ego of the third party, who thinks she's the original. I hate both my father and his mistress, but it's hard for me to confront him because he's our provider. I also don't want to create animosity. My father works abroad, and we don't care about their relationship when he's away, but when he's here, we just want to have some family bonding. The mistress doesn't like that, though.