I think that you have to find more than one way of playing the B chord, or parts of it, to suit different songs. If you are just strumming then putting your index finger on the high E at the second fret will be fine with one, two or three fingers on the 2nd, 3rd and 4th strings at the 4th fret. But if you are playing a R'n'R shuffle thing, then you will be wanting to do a stretch with your pinky and, as I've just discovered, with your index on the high E at the second fret, your movement is restricted - so try alternatives. For example:
a) Try holding down the second string (A) at the second fret and holding down strings 3, 4 and 5 with your bent 3rd finger at the 4th fret. Don't worry about the high E: your other fingers can damp it. This leaves your pinky free.
b) Try hooking your thumb over to hold down the 6th and 5th strings (E and A) at the second fret and using your other fingers to make the rest of the chord at the 4th fret. Don't let any traditionalist guitar teachers see you using your thumb in this way. (j/k)
c) Try substituting a B7 in the open position.
There's two things to note here. First, it is important to nail the A chord shape at the second fret to play the B chord because you will be using this same shape at different frets for all kinds of different chords. Second, even people with a full set of digits find the B chord difficult when they are starting out. It's a long time since I was learning but I remember thinking it was impossible: now my fingers flop down in the right place without me thinking about it. Perhaps with a shorter first finger you will have to think about it a little, but not too much.
The other thing that helps is turning the amp up a bit more. It won't make playing the B chord any easier, but it's more fun learning when you are playing loud.
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