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.
Indeed you did well by taking the initiative to apologize to that woman because of your mistreatment to her as the best of those who dispute is the one who starts saying Salaam to the other. Normally, she should have accepted your apology, as this is the character of the generous people who do not want to keep any rancor against others. Furthermore, she should not desert you more than three days for a worldly reason as this is Islamically forbidden as we have already clarified in Fataawa 84976 and 86772.
Hence, if she continues to desert you – while she has no Sharee'ah-based reason for doing so – then she is committing a sin. If she is a relative of yours, then she is cutting ties of kinship with you, but if she is not a relative, then she is not considered as one of your relatives by just being a wife to your brother.
However, there is no harm to continue trying to reconcile with her and if you do not succeed in doing so, then leave her and try to forget what happened and do not continue to think that her behaving in this manner constitutes insulting behaviour towards you.
Allaah Knows best.