at the outset, it looks like an intruder - but too much simply doesn't add up, and very basic detective work tells us that the theory is way too inconsistent. the note itself is bizarre (long and somehow accurately states a figure of $118,000, the exact amount the father received as a bonus, which is a really weird number for a random intruder to come up with, and the handwriting significantly similar to the mother's), there was no disturbance at the theoretical point of entry, no footprints, nothing to indicate an intruder. there was also no evidence of sexual assault - a minor DNA find in the panties blew it up as a theory, but there was no evidence of sexual assault in the autopsy to indicate rape or any other bodily injury; and the intruder killed the girl before leaving, which makes very little sense as well.
and, of course, the big kicker to the intruder theory were the two puncture marks on her body. the initial investigation speculated it to be a stun gun, but further investigation can clearly indicate those marks were wholly inconsistent with stun gun marks. the only thing that was a highly accurate fit was the train tracks, which were the exact width and size to make such a puncture (which is explained by the fact after burke bashed her in the head, he used them to poke her if she was alive or not).
so the intruder theory, while you can't outright dismiss, looks extremely weak. you have to go on the strength of the evidence, and there's not much to go with on this.
the theory that the mother killed her because she was so mad that the girl wet the bed also didn't have much weight. there was no history or evidence of past abuse, no evidence from the mother physically that she did it, and no evidence in general that she was the killer.
the brother, burke though - jesus, it just piles and piles on top of him. the most damaging really is the interview he has with the detective 13 days after the murder. it's borderline creepy to watch. i'd go on with the evidence that clearly supports a very strong theory that burke did it, but it's already a long post in general.
again, you go by strength of the evidence. in any criminal investigation, you don't outright dismiss any theory until evidence strongly points to something. and here, every theory is significantly flawed except for the brother burke being the one that did it. he had a past history of hurting her, he clearly has mental issues, had motive (jealousy and impulsive anger), and the physical evidence strongly lines up with him. the sad thing is that he can't be prosecuted b/c he was under 10 at the time, but the fact the DA blocked a lot of the investigation and intentionally derailed it should lead to him being prosecuted imo.