I think that discod is spot-on about Patsy's personality.
Here's a variation on the rage-killing that I think is plausible (this is a THEORY): John was molesting JonBenet. This was due to the combined stress of losing his other daughter Beth and his wife having cancer. Patsy caught him and went berserk. Instead of attacking her husband, she attacked her daughter, clunking her on the head with a heavy object.
She immediately regretted it. Both parents could tell how severe the injuries were and that JonBenet could not be revived, and stayed up all night staging a fake kidnapping. They strangled her from behind because they could not bear to look at her face. They put her in the basement and covered her up.
None of this can be proven, but I think it's the most plausible scenario.