(I hope I did this right. Please let me know if you see any errors that need fixing. Thanks)
The following may offer a perspective on the contradictions between reports of child abuse against JH and SH in contrast to the appearance of the family as portrayed online and to friends. In referencing these situations I am using JH/SH because I don't know if the abuse was done by one or both.
Excerpts in italics are from Wikipedia page about The cycle of abuse a social cycle theory developed in 1979 by Lenore E. Walker to explain patterns of behavior in an abusive relationship. Additional links below.
Comments in regular text are my opinions or observations only and are not based on any professional expertise.
Cycle of abuse
1: Tension building
Stress builds from the pressures of daily life, like conflict over children, marital issues, misunderstandings, or other family conflicts. (...) During this period, the abuser feels ignored, threatened, annoyed or wronged. The feeling lasts on average several minutes to hours, it may last as much as several months.
JH wrote often about the tension and stress she was going through. She seemed to have an ongoing laundry list of situations that put her in crises mode.
2: Acute violence
Characterized by outbursts of violent, abusive incidents which may be preceded by verbal abuse and include psychological abuse. During this stage the abuser attempts to dominate their partner (or child) with the use of domestic violence.
Speculation here is that JH/SH became increasingly frustrated when tensions built up and vented their frustration at the children. (According to reports made to CPS) There's no way of knowing how often this happened, but there were several reports made over the years.
3: Reconciliation
The perpetrator may begin to feel remorse, guilty feelings, or fear that their partner will leave or call the police. The victim feels pain, fear, humiliation, disrespect, confusion, and may mistakenly feel responsible. Characterized by affection, apology, or, alternatively, ignoring the incident, this phase marks an apparent end of violence, with assurances that it will never happen again, or that the abuser will do their best to change. During this stage the abuser may feel or claim to feel overwhelming remorse and sadness.
It's possible that JH/SH were genuinely remorseful for losing control of their anger. They may have sincerely expressed the desire to do better and promised each time that it would not happen again. During these times the children were taken on special trips given adequate food, treated with extra kindness. This would have been the time for photo shoots, videos, festivals etc. to show everyone (and to create online documentation that the were a happy loving family).
4: Calm During this period the abuser may agree to engage in counseling, ask for forgiveness, and create a normal atmosphere. However, interpersonal difficulties will inevitably arise, leading again to the tension building phase.
The calm phase would be when the food-fun-festival time is over and they return to everyday home life, tensions released exhausted and happy.
Once they are away from their public persona, tension begins to build again. Stress, illness, disagreements, the children growing up and testing the limits. Financial problems, social problems, it's always something. Eventually it gets to be too much and someone lashes out.
Additional thoughts: Escalation
During this last year it may be that some or all of the children were actively rebelling against their whole lifestyle. They wanted friends of their own, maybe they wanted to go to public school, or church. They may have challenged the "Moms" rejecting the plans they had for the future and arguing for the right to decide their own future. To JH/SH this may have seemed ungrateful, thus making the rebellious children targets for the indignation and wrath of JH/SH.
Here the cycle repeats in theory, but other factors seem to have brought it to another level. If Devonte and Hannah became angry, sullen (as teens often do) that may have triggered a major crisis. If these two ran away, as others have suggested, with CPS due to arrive the next day, JH/SH made have decided to leave them and run for the hills. They may have told the other children that they were going to get friends to help look for them. The situation ended in tragedy for the children.
Excerpts from:
https://en.wikipedia.org/wiki/Cycle_of_abuse
Links to other resources: Please note I am not endorsing all of the material on these links. They may or may not be helpful.
https://www.childwelfare.gov/learningcenter/
https://www.livestrong.com/article/100480-four-stages-abusive-relationship/
https://www.helpguide.org/articles/abuse/child-abuse-and-neglect.htm