The reason that I find that interesting is that I cannot help but contrast it with the end of the "Elly bans television because she blames it for her children cursing despite it being fairly obvious that her own habit of using language that would scandalize Lenny Bruce is the actual problem" arc in which Connie essentially tells her "Go on and blame someone else for your own stupidity like you always do. It's cool." This form of emotional support is also why Connie smilingly enables Elly's delusion that her children keep their room messy and listen to headache music to defy and torment her and not as a means of defending themselves from having their living space picked over by a lunatic who wants to erase their personalities.
Simply put, the reason that Elly loves having Connie around is that she is as ready to blame her children for her own catastrophic total failure as a wife, mother, daughter, citizen and multicellular carbon-based life form as Elly herself is. This means that she never need hear awful things like "Hey, dummy! Do you know what 'picking your battles' means?" or "Hey, stupid!!! Maybe you should actually listen to April about this Kortney person!" or even "Given that the more you shout and threaten, the less the kids are willing to talk to you or listen to what you have to say, wouldn't it be a good idea to calm down, quit acting like you're under siege and realize that maybe you've read them all wrong all this time?" It's easier listening to Connie and her "Go forth and be a shrill, belligerent, judgmental and ignorant wacko" because being stupid means never having to say "I'm sorry."