There is nothing wrong, as far as Islam is concerned, in giving Zakah to relatives as long as the person receiving this is financially straitened.
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states: Generally speaking, it is not at all considered necessary to tell anyone that what you are paying him/her is from Zakah. What is required of you is simply to ascertain that the person you are paying belong to the deserving categories of Zakah; once you have determined that, you don’t have to mention anything to him or her. In reply to someone who asked him, “Shall I tell someone that I am giving him Zakah?” Imam Ahamd replied, “Give, and remain silent; would you like to insult people?”

However, if you know of anyone who has a personal policy of not accepting help from Zakah funds, for whatever personal reasons he may have, then you should not give it to him, for we are certainly not allowed to offend people on such sensitive issues. But if the question arises: What if such a person is a close relative of yours and he is poor, and you find compelled on religious grounds to help him? The answer is: then there is another way out: You can still give him or her from your wealth and calculate the Zakahability after deducting that portion you have taken out. In other words, you consider it as your own basic expenses, for Zakah falls on you after you have taken that portion out. By doing this, you are not breaching any of the principles of Islam, for, according to Imam Ahmad, we are under obligation to look after our relatives—if we have the means to do the same.

Moreover, Dr. Muzzamil Siddiqi, former president of the Islamic Society of North America, states the following: It is permissible to give Zakah to the needy relatives. The relatives to whom Zakah cannot be given are wife, children, grandchildren, parents and grandparents. It is one’s duty to take care of them first and then if there is any money left and it reached the nisab of Zakah, then one should give Zakah on that amount. Thus, all non-dependant relatives such as brothers, sisters, uncles, aunts, nephews, nieces etc. can receive the Zakah if they are poor and need help. The person who gives the Zakah must make an intention that the amount he/she is giving is for the purpose of Zakah. The recipient does not have to be informed about it.
It is better to give charity to an individual in a respectful manner without hurting his/her dignity. Allah says in the Qur’an: (If you disclose your charity, it is well, but if you conceal it and make it reach to those who are in need that is best for you. It will remove from you some of your sins and Allah is well-acquainted with what you do.) (Al-Baqarah 2:271)