Step 1: Frame the problem. Sydenham chorea from rheumatic fever often will not settle with anti-inflammatory rheumatic therapy, so we treat the movements directly when they are severe or resistant.
Step 2: The two symptomatic drug families are anticonvulsants (valproate, carbamazepine) and dopamine-blocking neuroleptics (haloperidol, pimozide, risperidone).
Step 3: In a child with resistant chorea, sodium $\text{valproate}$ is preferred first because it controls the involuntary movements well while avoiding the extrapyramidal and sedative burden of neuroleptics.
Step 4: Eliminate the rest: haloperidol is reserved as backup, diazepam only gives mild non-specific relief, and probenecid is purely a uricosuric for gout and is irrelevant here.
Step 5: The drug of choice for resistant rheumatic chorea is valproate.\[\boxed{\text{Valproate}}\]