I'm not sure why he'd need to blackmail Asuna's mom, except as a way to ensure he can visit the house and stay over whenever he wants.
As for blackmailing Asuna? Well, I could see it happening. He has been collecting nude pictures of her for a while, but he's been showing them off on the pervert website anyway. I suspect the 'rainy night together' might give him new, super sensitive material to use. I just don't see him needing it, with the direction of their story as is. We already know Asuna is going to be super regretful over allowing the sex, but I can see her coming to crave Inoda sex quite naturally without being forced. He fucks way better than Kirito, with a much bigger dick and endless, horny stamina. After their night together, she's going back to her tiny dick, quick shot, one shot chump Kirito, and she's not going to be able to cum off it anymore. That's going to drive her wild, especially if Inoda keeps messing with her in FOG.
Like, how would blackmail even be used? Why would he need it? What would he get out of a blackmail arrangement that he couldn't get anyway?