What is the ruling of Islamic law on a wife who swore by Allah, saying, "By Allah the Almighty, or else I will lose my children, if a maid enters my house," and then wished to allow a maid into the house?

Swearing by the loss of children is not a legal oath and is impermissible. Whoever swears by it and then breaks it is not required to offer expiation, but must repent because they swore by other than Allah. What is considered valid is an oath by Allah the Almighty. So, if the wife wishes to bring in a maid, she must offer expiation for her oath.