My Sprachgefühl prefers "I would rather she came tomorrow", my feeling that it sounds right reinforced by the exigencies of the sequence of tenses. "Came" is past subjunctive here, though identical to the past simple.
"Come" (3rd person subjunctive) I would reserve to follow a verb in the present tense, also on the grounds of sequence of tenses, viz. "I insist she come tomorrow not today"(where "come" is present subjunctive. But I admit that one does hear No. 1 too in the mouths of native speakers.
I think Murphy's right, this is another BrE/AmE difference, although, as ever, we're not talking about absolutes.
It's always struck me that North Americans are much more comfortable with the present subjunctive than Brits; though I think we might, little by little and in certain constructions, be learning it back from them.