Sheila begs Frank to attend the Conferences with Karen in a totally sweet way -- "I just want someone to be there for her, to bear witness to her achievements" -- but he goes on another rant about how these nights are just about the teachers putting themselves on a pedestal so that you can worship them. It goes on at length and it's fairly gross, but we're building a pathology for Frank here where I think he's convinced that his failures in life are failures of the system -- I mean, clearly he's as much of a genius as Fiona or Lip -- and not his own failures, which means his insecurity about his fortunes becomes an insecurity about the system itself, because even Frank knows a diploma should be worthless considering his own intelligence.
But since that didn't work out -- him being an alcoholic and a disgusting, ridiculous person and all -- he feels like the whole world is looking at him and thinking he is ignorant, which he is not. And teachers are authority figures, which automatically puts all of his issues into projection mode anyway, not to mention the fact that they are in better contact with his kids than he is, and in a position to judge him for his parenting skills, which he can't handle at all, because he only sees his children as extensions of himself, and anything negative about them or that connection means negatives about him and nothing else, because they don't really otherwise exist.
Which is why Debbie is his favorite, because she has such a gift of compassion that she doesn't even look like the punching bag they all are, but which is also why Karen will benefit here, because she's both his child and not his child, and doesn't bear the taint of being an extension of him and therefore his own self-hatred. He can take all kinds of unworthy credit for how great she is, which he would do and always does with Lip and Fiona particularly, without having to deal with the downside of the ways he has irreparably damaged his own kids.
Anyway, the goons come knocking and Frank gets very scared, but Sheila just assumes it's the granola she ordered from Oregon, and then he busts out of there while she's stalling them at the door about taking off their shoes and all that. The lie is that they are on Frank's darts team and they're raising money for paralyzed kids. "He's kind of in an uncooperative mood today, but I'll see if the paralyzed kids can get him out!" She lets them in and is totally fucked up and sweet as usual, but once they're inside, Frank is of course totally gone. Luckily, I think that Sheila's innate awesomeness will keep her safe in a way that being jacked up-looking Fiona with the Killing Bat did not.