Question: I find when playing in a minor key I always end up playing the major version of the V chord. (So in Em I always end up playing a "B major" chord.)

However, the third of this chord should be played as a minor when looking at the key and it seems like using an accidental as frequently as I do is not really in the spirit of accidentals.

Am I making a mistake in my music theory? Am I playing the key I think I am? Is this just a mode? Do I need to start playing more B minors?

Please bear in mind I am relatively new to music theory and would appreciate it if you treat me like an idiot. Thanks.

Answer: 
Two points.

First: the scale of a key or mode is a framework. It doesn't instruct you NOT to use other notes. A piece of music that used ONLY diatonic (in the scale) notes and chords would be very basic and possibly very boring (although there's also beauty in simplicity).

Second: in traditional harmony the dominant chord of both a major or minor key is normally major. If we're writing the sort of music that deals in dominant > tonic relationships (and that's the bulk of Western music for the last few hundred years) the dominant chord NEEDS to tend toward the tonic chord. A large part of that tension comes from it including the 'leading note', the note a semitone below the tonic.

We don't HAVE to use major dominant chords. But we don't have to reject then either. You're doing nothing 'wrong' by sharpening that 7th into a leading note. Equally, you're doing nothing 'wrong' by investigating the sound of a minor dominant chord.

"Theory describes, it does not command".
Yes, you are making a mistake in the theory you know. Each major key sig. has a relative minor to go with it - C- Am: G- Em; Bb- Gm etc. Whilst the majors adhere exactly to the # or b in their key sig., minors cannot and do not.

That's because the notes that make up the minor scales vary in their 6th and 7th notes. It's the way they are. Take A minor. 6th note can be F or F#, 7th can be G or G#. In your scenario, E minor can have C or C#, and D or D#.

The D/D# anomaly makes the chord based on B either B minor or B major respectively. Both are quite acceptable, and both are used. The B major, as you find by using it and it sounds good to you, uses the leading note of D# to sound more decisive going into E minor, but there's nothing in the theory that says we must use that, or we must use B minor. Whatever fits better is what we should use. Please don't use theory as a set of *rules*. It's more a set of *guidelines*. Usual adage - if it sounds good, it usually is - whether the 'rules' get broken or not!