Is it permissible to renew the marriage contract without informing the wife's father, given the difficulty of apprising him of the divorce matters that have occurred?

It is not permissible to contract a marriage with a girl without the permission of her guardian (wali). If her guardian is in another country, he can appoint a Muslim in the girl's country to marry her on his behalf. If marriage is not possible through her guardian, then look for someone else, or refer to the Sharia courts if you are in a country where they are available.