Is it permissible for a divorced woman, whose brothers refused her marriage, to enter into a legitimate (Sharia-compliant) contract with the consent of her son, for him to be her guardian, until the suitor comes to her country to formally propose to her?

Your brothers do not have the right to prevent you from marrying. The presence of children is not a legal impediment, as the Sharia (definition) texts include women who were previously married (thayyibat) and those with children. The Prophet, peace and blessings be upon him, married Umm Salamah, and she had children. Your adult son has more right to arrange your marriage than your brothers. You can review the order of guardians (awliya'). Try to convince your brothers to avoid disputes, and seek help from some virtuous people. Also, investigate the suitor's religiosity and character, for the Sharia encourages marrying a righteous man.