You have a lot of problems to deal with. Insurance follows the vehicle, which the owner is out of the country. UNTIL they talk to the owner, then the owners insurance can pay or (not).
The driver who you state has insurance, (can't) do anything till the owners insurance makes a determination to pay or deny the claim. Only (if) the owners insurance denies this claim, then the drivers insurance would then be secondary.
You (can't) use your uninsured or underinsured insurance on (your) own policy, if you have that coverage, till your (own) insurance (verifies) either that the owner/driver has (no) insurance or not (enough) insurance to pay for your damages/injuries.
It is unclear if you are claiming injuries or car damages or both. If you have collision, then (your) insurance will pay for your car damages. If injuries, then your insurance (if) you have medical payment coverage or PIP will pay for your medical bills up to the limits that you bought.
So in effect you are in a catch 22, since everything will start with the owner's insurance and the owner's insurance MUST talk to the owner (before) they pay or deny your claim.
Yes, you can sue the driver, but if you do, then the driver's insurance must provide a lawyer for free to defend the driver.
retired auto adjuster