Is one absolved of responsibility before Allah for cutting ties of kinship by sending money to an aunt who refuses contact and asks to be left alone, while the father forbids it?

If a close relative of yours tries to connect with you, and she refuses, then there is no sin upon you, and you are not obliged to send her money. You are absolved as long as you tried to connect and she refused. However, continue trying in a way that does not harm your relationship with your father, and remind her of the impermissibility of severing ties of kinship. Sending her money if she is in need is a good deed for which you will be rewarded, and informing her of this might be good to bring joy to her and purify her heart. This is considered a permissible act of maintaining kinship ties.