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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If you can marry your maternal cousin while keeping your first wife, then this is the best so that you could please your father and family and fulfil the promise you made to the daughter of your maternal aunt. However, if you are unable to do so, then you are obliged to be kind and dutiful to your father and keep ties with your family and relatives with whatever you could, and then you will not be blamed for not pleasing them but you should inform the daughter of your maternal aunt that you are unable to marry her so that your engagement with her will be nullified and she will be able to marry another man.
Allaah Knows best.