Is Depakote a dopamine antagonist?

No. According to our current understanding, Depakote work by altering calcium current, sodium channel, and the synthesis and breakdown of gaba, the main inhibitory neurotransmitter in the brain.
No. It does not block Dopamine neurotransmission. It is believed to have a stabilizing effect on neural electrical hyperactivity, this it was developed to help control seizures or epilepsy. That is how some 'mood swings' may not be, strictly speaking, 'bipolar' as a seizure disorder of mood-regulating structures of the brain, the limbic system, could give you a very similar set of symptoms.