All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If you mean that your children were given the last name of their mother's family, then there is no harm in that; please refer to Fatwa 266275. On the other hand, if you mean that they were given another family name, like the last name of the mother's new husband, then this is impermissible.
In any case, this does not change the fact that you are their legitimate father. It is your duty to provide for them, and you inherit from them and they inherit from you. As for their school fees, most of the scholars held that school fees are not part of the obligatory financial support. This means that the father is not obliged to finance his children's education except what they need to learn to fulfill their religious obligations. However, you should finance their education because this may give you some sort of control concerning them. You are also advised to try to have custody over them as a non-Muslim mother has no right to the custody of the children.
According to the preferred view of Muslim jurists, being a Muslim is one of the conditions for custody of children. Please refer to Fatwa 86891. In addition, since your ex-wife has remarried, her right to custody to the children is forfeited.
If you cannot get custody of your children, you are advised to care for them and give them as much advice as you can so that they grow up with the Islamic beliefs and manners. It should be noted that when they reach puberty, they may live independently from their mother.
You should know that children whose parents are of different religions belong to the better of the two religions as underlined in Fatwa 81957. We also stress that it is impermissible for a Muslim to marry a non-Muslim unless she belongs to the People of the Book (Christian or Jew) and she is chaste; and it is better in any case for a Muslim man to marry a pious Muslim woman.
Allaah Knows best.