1. I won't have it! = I won't tolerate it!
2. I won't have them playing round here = I won't tolerate them playing round here.
You can think of "not have" here as an approximate synonym of "not put up with" or "not tolerate".
In #1, "it" is the object of "have".
In #2, the entire underlined phrase is the object of "have".
Does that help?