Oppositional Defiant Disorder (ODD) Support Group
Oppositional Defiant Disorder (ODD) an ongoing pattern of disobedient, hostile, and defiant behavior toward authority figures that goes beyond the bounds of normal childhood behavior. When a child cannot seem to control his anger or frustration, even over what seems to be trivial or simple to others, the child will often react in violent or negative ways to his own...

About other people opinion, you better start building up your armour against it, you need your strenght for other things.
Im a single mum and was pretty much alone with the kids before I divorced.
Try to get some help, ie do you have a relative that could take one of the kids every thursday afternoon or something like that. If you cant try to get some alone time with each child. And to do something fun.
Deside what is most important regarding behavior and try to ignore the less important parts, we cant be nagging all the time ;)
Also read some good books about ODD (helps you feel not so alone).
Hope this helps, you are certainly not alone.