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 is His slave and Messenger.
Your marriage is correct and it is not a betrayal to your first wife; for more benefit, please refer to Fataawa 82068 and 84411.
It is not a condition that your first wife knows about your second marriage in order that this marriage be valid. If the marriage took place fulfilling its conditions, like identifying the two spouses, their proposal and acceptance, and the consent of the guardian of the woman, and the presence of witnesses and the like, then the marriage is valid unless there is another impediment; for more benefit, please refer to Fatwa 83629.
All what a husband who has more than one wife is obliged to do is to be just between them.
As regards divorce, the permissible divorce that is in accordance with the Sunnah is one-time divorce that is issued by the husband to his wife when she becomes pure [to wait until she is not in menses] without having sexual intercourse with her. For more benefit, refer to Fataawa 82735 and 85415.
Finally, our advice to you is not to divorce your second wife and to endeavour to solve the problems that press on you to divorce. If you are not able to solve these problems, then you may issue divorce according to the conditions which we mentioned above.
Allaah Knows best.