Ask your insurance company.

    You will have to go over your insurance policy.  You will almost
certainly get coverage for restorative dentistry from your dental
policy, but most patients with dentinogenesis imperfecta need very
extensive treatment (as you no doubt already know) and with yearly
maximum benefits where most of them are set the dental insurance won't
go very far.
    Your medical insurance logically sounds like it MAY cover treatment
related to a genetic condition.  However, in my experience getting
medical to cover any type of dental treatment whatever the cause is very
difficult.  If your dentist is willing to make some calls and speak to
consultants it may be helpful in figuring out if medical may help.
Persistence pays--the first people you get on the phone say "no" as a
visceral reflex.  Try to talk to a supervisor (or have your dentist do it).

Good luck,
Steve

Check your actual medical plan language. It will have language about when or
if it ever covers dental care. Some basically say no, never while others may
leave some openings that would allow for consideration of your situation.

T