Can you clarify where the second vet got this number from? "0.5 mg/kg x 0.03 kg of hamster) = 0.015 mg" - where has 0.5mg/kg came from?
I'm not a vet - I took some clinical classes two years ago, so I'm rusty - so I don't mean to question them. It's just I do not see where and why they're using 0.5mg/kg when the vet has
not prescribed you 0.5mg/kg, but instead has prescribed you 1.5mg/kg. She would be right in saying that 0.01ml would be the correct amount
if we were talking about a 0.5mg dosage. But we are not, your vet has
prescribed you a 1.5mg/kg dosage, in which case, 0.03ml is the right amount.
Because I'm getting;
(1.5mg/kg)(0.03kg) = 0.045mg.
When using the 1.5mg/ml; (0.045mg)/(1.5mg/ml) = 0.03ml.
I totally understand your reluctance to trust the first vet, and believe me I would be the same, but although she made a ridiculously silly and dangerous mistake with the syringe readings, I can't see anything wrong with the prescription she's given you.
eta; I just bolded some important parts ^ just because we're talking about an animal clearly in some level of pain, so while its important that he's not be overdosed, it's also important that his pain is being appropriately managed.