Vehicle insurance data is stored on the Motor Insurance Database - the second insurer would probably give your son a policy on the basis of him being the policyholder, but they have to put this policy on the database within seven days, and so would find out that the car is dual insured - they would then cancel the policy ab initio (from the beginning).
The idea of having you both on separate insurances is not a wise one, it doesnt make sense, if he wants his own policy to start his own no claims discount then just be a named driver on the policy (insurers may ask questions into the ownership of the vehicle (insurable interest) - although a son being the policyholder and main driver on his fathers car is generally now widely accepted).
Or, just cancel your policy and find a cheaper one for you both using your no claims and him as a named driver. (find the cheapest quote before cancelling though obviously lol)