Hopefully the hire company’s insurance will take care of your claim, then trying to claim it back from whoever was driving. I think that’s usually what happens when an insured vehicle is driven by an uninsured driver.
It’s not that simple… Once and insurer assumes a risk they’re stuck with the legal minimum.
If we suppose the mother hired the vehicle and then permitted her son to drive it (it doesn’t matter that she didn’t declare him at the time of hire) then the minimum legal insurance (3rd Party) will still be valid.
The only way the insurer could wriggle out of it would be if she declared that he has taken the vehicle without her permission, in which case he will be guilty of TWOC (taking the vehicle without consent) and it’s unlikely that she will do that as she wont want him done for TWOC.
If the driver hired the vehicle and it later comes to light that they made some sort of false claim then insurance would still be valid as the insurer has assumed the risk. Insurance cannot be magically voided by virtue of a false representation… it has to be cancelled… this is one reason why it’s so expensive.