Well, I can't really say I have ever been in a situation similar to this, but I'll try my best to be empathetic. hmm.
I suppose if I was in a similar situation I would confront my mom. I would make sure my dad was out..for a while, and I would bring her to the computer and start playing the video. She has a right to know that you know. This is probably going to be terribly embarrassing for both you and her, but once you get past the embarrassment, it's possible that you will get some explanations. Hopefully these videos were given to your mom BEFORE she got back together with your dad.
Even though this is probably really awkward for you, its important that you don't judge her. She's a grown woman, and what she does on her own accord is her own business.(assuming she isn't cheating on your dad). Try and be a little open minded, and make her as comfortable as possible while she is explaining this.
So usually when I say this I only halfway mean it, but honestly, this time i mean it 100%. PLEASE be sure to let me know how this situation works out for you. I'm very interested.
Good luck with your family! :D
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:)