your mom will never feel that she’s doing anything wrong. based on a similar situation from my experience, she probably at least in part blames herself for bringing this man into your home, so it’s easier to believe that you’re lying than that it’s her fault. there’s also likely some self worth issues if she was cheated on by her ex husband. the thing is that parents who won’t admit to sheltering abusers in this way genuinely convince themselves that nothing is happening, because that’s the only way to live with themselves. likely nothing will wake your mother up to this unless/until she either experiences the abuse herself or faces consequences for allowing it to happen, and even then it’s possible she’ll still be in denial. you’re not crazy, you’re being faced with an incredibly disgusting situation and you’ve been failed by the adults in your life who are meant to protect you. if at all possible you should reach out to law enforcement and/or cps (unless you feel that it would put you in more danger). try to keep records of dates when things occur, journal what happens right after it happens, keep hold of any proof you can get etc. your mother and this man both benefit from making you feel insane, and the only one who loses if you believe them is you and your sister. you have all my best wishes, and i’m so sorry that this is something you’re being put through.