What should I do about my relative who does not want to speak to me after I apologized to her, and am I considered sinful for her unwillingness to communicate with me?

Since you apologized to your relative and did not sever ties with her, you have acted rightly and excellently, and there is no sin upon you. If you remain diligent in maintaining ties with her and being kind to her, you are upon a great good. If she continues to sever ties with you, she is in great peril, due to the hadith (definition) of Abu Hurayrah: "Indeed, I have relatives whom I keep ties with, but they sever ties with me; I am kind to them, but they mistreat me; and I am forbearing with them, but they act ignorantly towards me!" He (the Prophet) said: "If you are as you say, then it is as if you are feeding them hot ashes, and there will always be a supporter from Allah with you against them as long as you continue to do that."