Is it permissible to marry a woman by entrusting her guardian to a trustworthy man to solemnize the marriage in another city, if it is impossible to propose to her due to animosity between the two families, and if her brothers refuse to grant authorization, would the city’s judge be considered her guardian?

There is no objection to the conditions you have stipulated for the woman you wish to marry. If her guardians accept delegating others, the marriage is valid if its conditions are met. If they refuse to delegate others, they have that right, because the guardianship of marriage is their right and is not forfeited except by a legitimate cause. If you are suitable for her and she agrees to marry, and her brothers prevent her marriage without a legitimate cause, then this is an act of 'adhl (unjust prevention of marriage). She has the right to refer her case to a Sharia judge outside her country if it is difficult to do so in her country, for the ruler is the guardian of those who have no guardian or whose guardians have prevented them from marrying.