In Euchre, Can a person of the opposing team go alone if trump was ordered up by the other team?
According to both the Bicycle Card Company Rules and the EuchreLinks.Com website Rulee only the person actually naming the trump denomination, termed the maker, has the option of going alone.

Playing Alone
If the player who fixes the trump suit believes it will be to his side's advantage to play without the help of his partner's cards, the player exercises this option by declaring &quot;alone&quot; distinctly at the time of making the trump. This player's partner then turns his cards face down and does not participate in the play.

Or

The player, who chooses the trump suit, either by accepting the up-card's suit as trump, or by naming a different suit, is called the maker. Before the play of the hand begins, the maker may announce; &quot;Alone&quot;, in which case the maker's partner places his hand facedown and does not participate in the play.

Note that both these Rule compilations do not include your House Rule of a card being passed from maker's partner to the maker.