The second part of your thesis is correct...The woman in this case has committed adultery because she married while her husband is still alive.
Mark 10
11 He answered, “Anyone who divorces his wife and marries another woman commits adultery against her. 12 And if she divorces her husband and marries another man, she commits adultery.”
1 corinthians 7:10
To the married I give this command (not I, but the Lord): A wife must not separate from her husband. 11 But if she does, she must remain unmarried or else be reconciled to her husband. And a husband must not divorce his wife.
1 Corinthians 7:39
A woman is bound to her husband as long as he lives. But if her husband dies, she is free to marry anyone she wishes, but he must belong to the Lord.