You should find out what will result from the civil divorce such as rulings having to do with children, inheritance, mahr and maintenance. If you have a child, will you be able to attribute him to his father? If one of you dies, will the other be able to inherit? How will you be able to prove your rights to maintenance and the deferred portion of the mahr, if there is any?
If you can avoid these negative consequences, and the possibility of your husband going to prison is a real one, then there is nothing wrong with you getting a civil divorce.
If the civil divorce does not involve your husband uttering the words of divorce (talaaq), and he signs it or writes it without the intention of talaaq, then it does not count as talaaq. This has been explained previously in the answers to questions no. 127179 and 72860
We advise you to have your marriage and your rights documented in a way that counts, such as doing the marriage contract in the Islamic Centre after the date of the divorce, if that could be of benefit, or documenting it in your original country or in another Islamic country, if that will not result in the problems that may result from documenting your marriage in the American courts.
We ask Allah to make things easy for you and to help you to obey Him.
Our advice to your husband is not to neglect the rights of his first wife and her child, and not to leave her hanging. Rather if he wishes he may divorce her or if he wishes he may keep her and give her her rights, unless she herself agrees to waive them.
And Allah knows best.