Every car insurance company is different and has different guidelines so I can't speak to what your companies policy on refunds are specifically. Typically if you cancel your policy within days of starting it, you would receive some form of a refund.
This has more to do with company-specific guidelines. While some companies will prevent you from seeking full reimbursement for canceling a policy within 90 days, others will not if you can show proof of other insurance.
The state of Florida requires that insurance companies refund at least 90% of the unearned premium paid by a customer if they receive a request to cancel. There are instances where a company may include the policies fees within the first month so your refund can vary depending on which company you're with.
There is no guarantee of a refund, so you would have to contact your insurance provider to find out if you are eligible for a refund as each company operates a bit differently with policy cancellations in the first month of coverage. The same thing goes for whether or not they will notify your lien holder of the cancellation.
Each company is a bit different in how they refund policies. However, since your vehicle was returned, you might be eligible for a full refund if you submit some sort of proof to the insurance company that your vehicle was defective.