So the sister abandons the brother at the park AFTER she realises he's knocked out, goes home to WAIT for the mother, both of them decide to go back to the park WITHOUT CALLING FOR MEDICAL ASSISTANCE! All of this taking at least 2 hours (see how there's some color in the sky when the sister pushes the brother but it's pitch black when she returns with the mom).
While the sister's actions could be explained by her being very young and ignorant (she's probably like 5-7 years old and probably couldn't lift/move her brother), the mom is EXTREMELY IRRESPONSIBLE! Her daughter whilst COVERED IN BLOOD tells her that her son is BADLY HURT (UNCONCIOUS even), and she decides to GO TO THE PARK instead of CALLING FOR MEDICAL HELP! Mind you the mum KNOWS that her daughter had been WAITING FOR HER to come home and she KNOWS her son is so BADLY HURT that he CAN'T COME HOME! She must assume then that a significant amount of time hss passed since her son got injured. So why wouldn't she call for medics immediately to cut down on the time he spent untreated and reduce the likelyhood that he'd die?
There's actually a pretty reasonable excuse on the mom's action.
Short explanation: Panic/Nervousness.
Long explanation:
You can't really expect someone who isn't a trained personnel to respond well in an emergency situation. Imagine hearing your son's got badly injured, that'll very likely put your mind in a jeopardy which will affect your ability to think rationally. In such scenario, what the mom did is probably purely following her instinct to see whether her son is okay or not(which obviously he isn't, but remember, she couldn't think straight atm). Also, while what the mom did isn't ideal, it isn't the worst that could've happened either, since there is also a possibility of her having an absolute breakdown and did nothing but panicking.
As for the sister: Yeah, just a kid being a kid, nothing much to expect.
PS: I do agree that the mom might've a few screw loose (at the current timeline) but that is probably because of depression after her son change of personality (sort of), which I assume didn't happen yet on the timeline when this incident occured.