This thread reminds me of that Burgerking commercial with the guy with too-small-hands. I lol'd.
But anyway, OP...
Some other people already mentioned it, but I'm going to re-iterate it because it's true. Your hands aren't too small for the instrument, they're just not flexible enough. Work on being able to spread out wide and being able to stay coordinated in those wide spread positions.
It takes a while, but gradually you'll start noticing that it's much easier to make chords you had trouble with before. It doesn't happen overnight, but if you do your exercises every day, you will improve.
Unless your hands are like, baby sized, or you have no fingers, then you're not doomed.
__________________
|