How can a wife be persuaded to accept polygyny, given that the husband's intention is to marry a widow and care for her children, without hurting her feelings?

Women's jealousy and their dislike for co-wives is something they are inherently predisposed to, and even the Mothers of the Believers were not immune to it. So, there is no surprise in your righteous wife's jealousy at the idea of polygyny. If you are determined to practice polygyny, then proceed with it if you are capable of fulfilling the rights of all. Try to convince your wife of the benefits of polygyny and that your marriage to another will not affect your love for her or your responsibility towards her. Show affection to her with gifts, for "exchange gifts and you will love one another."