I intend to marry a second wife without informing her of my first wife, and also without informing my first wife.

Answer

A second marriage will be valid without informing the first wife. It will also be valid even if the second wife is not informed of the first wife. While the marriage will be valid, the consequences of secret marriages are almost always misery and heart-ache. A marriage is bound to become known sooner or later. It is compulsory to mete out equality of nights and expenses to both wives. If a man fails in these aspects, then the punishment is severe in the Hereafter. When the husband has to sleep at the home of the second wife on a regular basis, the first wife will most certainly become suspicious, and similarly will the second wife when she sees that her husband is regularly sleeping out of the home.

Also, what will happen with the children of the two wives? It is not permissible to conceal the fact of children from the wives because it could happen that a boy later in life marries his own sister (the daughter of the other wife) since he will not be aware that she is his sister.

Furthermore, is the issue of inheritance. The children of both wives and the two wives themselves will inherit in the man's estate. If the marriage of the second wife is not known, then she and her children will be deprived of their inheritance. So while the marriage to the second wife is valid without informing the first wife, it is not possible nor is it permissible to keep this information a secret for too long. It is also not permissible to deceive the second woman. She must be told of the first wife.