All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The fact that divorce took place in American courts does not change the Islamic ruling regarding the topic in question, which is the effectiveness of divorce, so far as your husband had uttered that he divorced you. The only person who makes a divorce effective is the husband. Courts only add their official stamps to the decision.
As for the question of regarding the statement of divorce made thrice on a single occasion as meaning an irrevocable divorce, the view of the majority of the scholars, including the Four Schools of Fiqh, is that the statement of divorce made thrice on a single occasion is regarded as statement of divorce made on three distinctive occasions, and is therefore irrevocable. After this, the woman becomes unlawful for her former husband until she marries another man and the marriage is consummated and she is divorced again. It is then that the former husband can marry her with a new marriage contract after she has finished her waiting period. This is the safest opinion.
Some Hambali scholars like Ibn Taymiyyah, Ibn Al-Qayyim and other contemporary scholars who agreed with their opinion, like Shaykh Ibn Baz and Shaykh Ibn ‘Uthaymeen, said that, ‘The statement of divorce uttered three times on a single occasion is only regarded as one single statement of divorce and is therefore revocable.’
Both opinions have their respective pieces of evidence that cannot be explained here in details. However, we will give you the proofs relied upon by Ibn Taymiyyah and those who supported his opinion, that you might see a way out through it.
Imam Ahmad, Muslim, and others reported on the authority of Ibn ‘Abbaas that he said, ‘The pronouncement of three divorces during the lifetime of Allah's Messenger and that of Abu Bakr and two years of the Caliphate of ‘Umar (was treated) as one.’ But ‘Umar bin Al-Khattab said, 'Indeed, the people have begun to hasten in the matter in which they are required to observe deliberateness. So, we have to effect it for them [i.e. regard it as three divorces, thereby making it irrevocable], and he effected it for them.
Nevertheless, we advise both of you to consult a trusted Sharee’ah authority like an Islamic Centre for a practical solution to your problem.
Anyway, you are Islamically divorced from your husband. So, it is unlawful for you to be in seclusion with him. It is also unlawful for you to engage in things that are forbidden between a non-Mahram man and a non-Mahram woman. You can talk to him regarding matters affecting your children and the like. But if the new marriage contract is made between both of you on the basis of this Fatwa, there is no objection if it is kept hidden from the other wife, for informing the first wife is not a condition for the validity of a marriage.
Allah knows best.