Is what a mother believes to be a nocturnal vision after spending the night the correct way for Istikhara, or is there another way to know its result?

The matter of Istikhara (seeking guidance from Allah) was brought by the Sharia, and the Prophet, peace be upon him, clarified its procedure. Do not refer to people's whims in it. It is not a condition for a vision to occur after Istikhara, and even if one occurs, it may not be an indication of its outcome. What matters in Istikhara is the extent of facilitation for the matter for which guidance is sought. The preponderant opinion among scholars is that proxy (niyaba) in Istikhara is not permissible. The difference in nationality between a man and a woman is not a legitimate impediment to marriage. The most important things to consider are the woman's religiosity and character. If the woman is righteous, we advise you to try to convince your mother to agree to your marriage to her. If she agrees, then praise be to Allah. Otherwise, you are not permitted to disobey her, and obeying her is obligatory unless it conflicts with a preponderant benefit.