As a native speaker of English, I find both of these sentences grammatically correct, but I would use them in slightly different circumstances. I would use the first when my father had already arrived:
"My mother said we would have dinner when my father got home. Well, he's been here since six o'clock and we still haven't had anything to eat!"
I'd use the second if we were still waiting for him:
"My mother said we would have dinner when my father gets home. He should be here by six; in the meantime, why don't you have a chocolate bar?"
I make this distinction intuitively, but I would think there are textbooks of English grammar and usage that would support it with formal analysis.