I don't necessarily believe the killer is a psychopath - no way of knowing that. Plenty of people do heinous and unthinkable things and they aren't psychopaths.
If the killer then went about their daily life with no outward signs of distress, I'll change my mind I'm fascinated to know how they behaved afterwards.
ETA: I always want to know what their family, friends or colleagues noticed about their behavior in the hours, days and weeks afterwards.
I also find changes in behavior to be very interesting, but may I respectfully add a different view? Wouldn't it almost be normal for the killer to 'flip the switch' and return to their normal routine? Like put that awful event into a box in your mind and compartmentalize it - dissociate that whole memory from the rest of your life? Then they wouldn't seem too different to an outsider. Now, at some point in the near or far future, that compartment may well burst open with a lot of feelings that need to be dealt with, but I think returning to the everyday routine may help to block out the horror of what the killer has done.
For this same reason, I think saying that a mother couldn't commit a crime like this is hogwash. The most dangerous member of any species is a mother who feels she needs to defend her young. I'm no criminal or even a particularly violent person, but I know I could kill if my loved ones were in mortal danger. I wouldn't enjoy it and I have no idea how I would deal with the aftermath, but there is not a doubt in my mind I could. Since I do feel this is a female perp, maybe she felt this same way - but she somehow convinced or rationalized to herself that Missy represented some kind of 'mortal' danger to her or her family unit. I am ABSOLUTELY not saying this was a reasonable rationalization for the perp to reach, but clearly we are not talking about a reasonable person. But I doubt we are talking about a psychopath - as they are unable to care about others. I think we are dealing with someone who cared all too much about someone(s) else.