Graduate application: Institutions that I have attended
Safest stance: mention both. 

School B may be "irrelevant to my major", but mentioning it is going to add to the application. Though we are talking about an application here, and not about a CV, something related happens in a typical CV too. You assign more significance to stuff that is more relevant to your major, you put a general heading Other relevant information, and include other not-so-relevant bits over there. Over here, you need not put a separate heading. but still, mentioning it (with a clear pronouncement that you've done it though it ain't directly relevant to your major), can only add to the application. What do you lose by mentioning it!

As far as the issue of transcript from B is concerned, apply for the same - that would serve the purpose of authentication. If there isn't enough time to get it before the application deadline, write an email to the department saying that you have applied for the same on ( insert date here ), and some delay in receiving it is anticipated. If possible, you can forward the application (for the transcript) too, along with this email, to serve as a direct confirmation. Maybe, you can also add that you will communicate the same as soon as it is received. That would be a correct and safe statement. And I don't think your masters-degree-school will consider it a wrong stance, since the crux of their decision will certainly not be based on this part. This is only going to be a point in your favor (if it does count at all), but certainly isn't the bone of contention for your application.