Okay I'm confused, correct me if I'm wrong because I was save transfering for some time but wasn't it Julia that gave Linda a push to finally sleep with MC? So why would they hide it from her and come up with excuses when caught by her? Wouldn't it make more sense if it was Emily that sudddenly came into the room?
I think if you're going by the conversation Julia and Linda have early on, yes Julia was trying to talk Linda into it but that might've been because Julia thought that Linda already wanted to do it and just needed confirmation from someone that it was okay. But at that point in the story, Linda still thought it was wrong and was looking for other solutions to dealing with MC's apparent attraction to her. She did eventually come around, obviously, but seemed to be willing to pursue the relationship despite her own personal moral objections, which is why she initially wanted to keep it hush hush.
I think the bigger discrepancy is that in the more recent term, Linda has been much less discreet, and although she continues to tell MC that they need to make sure not to get caught, we've seen her care less and less about getting caught and even thinking maybe it would kind of be hot to get caught. I the discrepancy between these thoughts and her reaction might be, at least in part, due to the fact that she and MC were done and already recovering from their intercourse. Linda's so far only had thoughts about how exciting it might be to get caught during intercourse, so the excitement for her may have been gone. I suspect it might be that the final push into sharing MC will be getting caught in the act and finding it a turnon.