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.
First of all, may Allaah reward you for being keen on asking about matters pertaining to your religion, and we ask Allaah to guide your father and sister to Islam. You should earnestly supplicate Allaah to guide them, and be keen on calling them to Islam. You should show the good traits of Islam to them especially by your conduct with them. For more benefit on Islam that it is the true religion, please refer to Fataawa 88906 and 81979.
Moreover, it is Islamicly permissible to keep ties with non-belligerent non-Muslim relatives and be kind to them, especially your parents. Allaah Says (what means): {Allaah does not forbid you from those who do not fight you because of religion and do not expel you from your homes — from being righteous toward them and acting justly toward them. Indeed, Allaah loves those who act justly.}[Quran 60:8] Besides, it is permissible to gift a non-Muslim and accept gifts from him.
Therefore, it is permissible for your children to accept the gift of their grandfather and maternal aunt if these gifts are not of the kind which are forbidden to take. Also, it is permissible for you to gift the children of your sister if this is not on the occasion of their birthday, and you should gift them with the intention of encouraging them to embrace Islam. For more benefit, please refer to Fatwa 85180.
Also, for more benefit on celebrating birthdays, please refer to Fataawa 106623, 84957 and 81725.
Allaah Knows best.