I think having had 2 children with another woman not his wife would certainly qualify as adultery.
In most states, common law wife is dependent on length of the relationship as well as offspring.
However, you're attempting to split hairs. The core of the argument is that this "man" lives with another women, with whom he has 2 children, has announced boldly that he plans to marry her as soon as Terri dies. Such a nice boy...