What is the ruling of Islamic law regarding the questioner's retrieval of the remaining amount from her cousin's daughter, who took half of the money sent to the orphans and the widow, and is the questioner considered to be in error for doing so?

If the donor specified that the money is for you and your children, then it is not permissible for the agent to spend it on others or to take it for himself, and your demand for it is valid. However, if the donor did not specify a particular poor person, then the agent may distribute it as he deems appropriate, and he may take from it if he is poor. In this case, the agent is not obligated to give all the money to you.