Is a wife considered divorced if she opens a Facebook account after her husband swore, saying: "It is unlawful for me and I divorce you if you open an account or even come close to it, whether directly or indirectly, in which case I will end what is between us," knowing that she opened his personal account to discover his conversations with other women? And does divorce occur if she uses her children's account to communicate with her family with her husband's knowledge?

This is a suspended divorce and a prohibition contingent upon your opening an account or getting close to it. A suspended divorce or prohibition takes effect upon the occurrence of the condition it was suspended upon. So, if you do what your husband intended, the divorce and prohibition will occur. The determination of what was intended by the prohibition refers to your husband's intention: whether he intended divorce, Dhihar (analogizing one's wife to an unmarriageable relative), or expiation of an oath.

Regarding your statement: "And if I use my children's Facebook account to communicate with my family, with my husband's knowledge, would I be divorced?" This refers back to what your husband intended by his oath. In addition to this, if he forbade you for a reason and that reason ceases to exist, no breach of the oath occurs. Thus, intention and reason have their effect on the oath.