>expecting a paranoid alcoholic to make rational decisions
Even though it's actually toned down in the show, it has been apparent for the best part of three seasons now that Cersei and her sanity are parting ways at an accelerating pace, which is not helped at all by her ever-increasing wine binges. She was an amoral plotter and heavy drinker already before, but Joffrey's death was the breaking point - she basically lost it and sees enemies everywhere and gives zero fraks because she's psychotically obsessed by "Maggy's" (12-year old's translitteration of "maegi") prophecy (the death of all her children, the younger and more beautiful queen displacing her, and the valonqar strangling her to death, latter being omitted from the show) and tries to desperately prevent it (yet is half-resigned to the idea of the prophecy being unavoidable), and soothes her suffering with more wine.
In the books, this is even more pronounced, she goes full-on Stalin and basically whenever she feels someone is not supporting her enthusiastically enough she tries to have him/her killed, often relying on overly complex plots whose success rate is about the same as those of one Wile E. Coyote. It's not like arming a violent cult just to curtail the influence her daughter-in-law has on her son is an idea that could go wrong in any way...
The irony is of course that it is her own actions to prevent the prophecy that fulfill the prophecy: she never said "no" to Joffrey which led to his assassination (since Olenna understandably wants to protect her granddaughter from the Westerosi Psycho Jr.), she starts meddling with Dorne that probably will lead even in the books in Myrcella's death, and when trying to destroy the cult she raised, she blew up Tommen's wife, mentor, in-laws, uncle, and at this point, Tommen may not even know that she was not in the Sept and he always was the too sensitive one, so what did she expect really. Also, by killing and betraying left and right, she's created so many angry younger siblings (which valonqar translates to) that practically anyone (besides first-born) could fulfill the prophecy of the valonqar at this point (she's herself still convinced it's her valonqar and it's Tyrion, not Jaime who is also her little brother).
