@carrie,
You'll sort it out -- with the help of a good counselor, if necessary.
On the question itself, both my Chicago Manual of Style and Garner's Dictionary of Modern American Usage are silent. Instinctively, I would say that both constructions are grammatically correct, but slightly different in content. To me, the phrase "I'd rather you come" implies "... and you probably will", whereas "I'd rather you came" impies "but you probably won't". In other words, I think of the "I would rather" construction as a contracted conditional, whose expanded form is "I would rather
if you come/came".
But that's just my intuition. I have no authority to back that up with.