Respond with love, not anger
Some typical scenarios and how to respond:
She hoards food. By following the trail of a nasty smell, you discover a cache under her mattress. Don't shame, scold, or punish; that reinforces her need to be in control. Ask her each morning to help you clean up the food. Repeat each time in a loving way that she can have food whenever she wants. If you catch her as she's taking food, put her on your lap and make a game of putting food into her mouth. If she won't let you, find some other way to feed her, eventually so that you are also lavishing her with affection. Your message: I am always here to give you what you need.
He doesn't listen. This is likely a purposeful behavior designed for you to lose control. Don't punish or repeat the request. Pick up the toys yourself: "You seemed really busy, so I cleaned up." If he asks, "Where's my black car?" tell him, "Gee, I put your cars in your room. I don't remember where that one is." The message he gets: If I want to know where my toys are, I better do this myself. Or, be a team and do chores together, yours and his. Make a chart of things you do well together and show it off to everyone. The message he gets: We have more in common than I realize.
He has frequent temper tantrums. Don't talk to him or put him in a time-out (isolation confirms that he is unlovable). If possible, scoop a young child into your arms and give him time-in, that is, time with you, where you carry him around: If you can't pick him up, stay with him until the tantrum passes. Sit an older child next to you and give him paper: "Can you draw your anger?" Your message: I will not leave you, even when you are angry and in pain.
She's flirtatious with men, mostly sitting on their laps or caressing their face. This is a serious behavior not only for what it may point to in her past but also because it puts her at risk for being victimized in the future. Don't ignore it or wait to talk about it afterward. Label it at the moment ("Stop flirting.") and interrupt it. Lift her off the man's lap, if necessary. If she won't come, reach for her hand and leave the room. Avoid anger. Your message: I'm the one who loves you. 