They ought to have a law against this type of abuse. That's part of the problem. The parents or guardian, need to shop, sure, but they ought to be looking after the child properly, and take them out when they are relaxed or open to it. Once they start crying the parent, supposedly smarter and more mature, ought to remove the child from the premises or take the child home. Children cry because they are tired and frustrated. Crying is the signal, "I'm not happy, Jan", so the it's up to the parent to remedy the situation. Not by hauling the kid around in a distressed state. That takes planning and com mun ic ation.
Keeping up with the Joneses isn't about giving in and doing what everyone else does because of a "if you can't beat them join them" mentality. Maybe some ed u cation needs to be involved, so that good behavioral skills start being employed rather than denied. Learning from example, when the examples we see are negative, leads to negative behavior being repeated and reinforced. It incorporates taking some responsibility for, not only your own actions but situations around you that you have some ability to impose control over.
As is usual, the previously innocent bystander, who tried to seek some intervention from the responsible adult on more than one occasion , is subject to the law. In the meantime, the cause, being the mental and emotional abuser, is allowed to continue unabated and without suitable consequence for the action or, in this case, lack of action on their part.