I am a giyores living in America. My brother and his family have been very supportive since my becoming Jewish. They have sent me gifts for Chanukah every year, even though I have asked them not to, and tried to explain to them very gently (and incompletely) that I cannot reciprocate by giving them gifts for their December holiday. Now that I have a son, they have sent him gifts too. Should I send their son, my nephew, something for December 25, so that as goyim they won’t get the impression that Jews will take, but not give? And also just to keep positive family relations including between my parents and other siblings? (Nobody else in my family sends Chanukah gifts.)
I do not feel that there is anything wrong in sending gifts to your relatives, even though they are non-Jewish. Perhaps, it would be wise to send them birthday gifts or other occasion gifts rather than December gifts. Best wishes.