I really don't think using profanity in front of kids is the same as talking about actual sex acts, whether or not some of the words overlap. Denise never said she was concerned about swearing; what she said was to chill on the loud sex talk with the kids nearby. So, IMO, she's not being a hypocrite by swearing or by quietly talking about a damn dick. And Kyle flat-out admitted that she understands not talking about certain subjects with her own kids around, so she should understand what Denise's issue was--and I say "was," past tense, because she'd probably be over it by now if they'd all let the shit go instead of trying to come up with new and innovative proof that she's hypocritical. She said to quiet down and they are, for some reason, scandalized and butt-hurt by it.
Also, the various reasons for her kids not being there are not necessarily an indication of prevarication, considering that they were simultaneously true.
It looked to me like like a boy-short bathing suit bottom, not a thong. I don't see the issue with it, as it was similar to a swimsuit cover-up one would wear over at a beach or pool.