If I were leading Alliance B, I would probably try and use one of my own members to spy on said nation, unless I was unable for some reason or another. Then I would use a trusted ally if they had the ability.
As for whether trust would be lost or not...I'm not sure it would be. Considering I'd be using the means available to me that happens to be a trusted ally, I would hope my members would be fine with the decision and understand where I'm coming from. But again, I would probably need a reason to use an ally over one of my own members.