I do not think these children are strong willed, I think the parents are too laid back.
The parents do not realize these children as begging for rules, expectations and guidance. This is a gift they give their children.
Children like knowing the rules.
They like being rewarded for being good, but they also like to be corrected when they are "not doing it right".. It gives them comfort that someone cares enough to help them correct this behavior.
It is like if you and I were about to cross the street and you did not look both ways , but I grabbed your arm and said , "hold on a car is coming!"
I may say it angrily or in an upset voice, may even yell. I am not mad at you I am concerned for you. I would then say, "wow, you need to remember to look before you cross."
This is the same thing each time a parent corrects or raises their voice to remind a child, "we do not act like that."
Also it takes a very strong person to be able to wait out a child's behaviors.
Time out for 10 minutes facing a corner and not allowed to make a sound or get up.. can take much longer, when the parent is willing to stick with it. If that child gets up, the parent places them back and the time begins again. No matter how many times or how long it actually takes.
Telling a child."I cannot hear crying. I cannot hear whining" and truly, closing the door and walking away EVERY TIME will work.
It is always a test with children.
Before going to the playground, state the rules. You will use good manners, you will share, no kicking, no hitting. If you break these rules we will leave.. And then do it.
Going to the grocery store.. Tell the child "Pick a snack and a drink, we do not buy treats at the store. You will sit in the basket. We are only purchasing what is on the list. " If you do not follow these rules we will leave and not have any groceries".. And then do it.
I am going to PM you my rules for tantrums and whining.. I think the moms on hear have read it so much they are sick of it..
Let your friend know She can fix this. It takes a lot of energy and dedication on her part.