什么“exclusion " ?

If the other driver is excluded from the other insurance, (many teenagers are excluded from their parent's policy to get the premium down) this case becomes a case with uninsured motorist, your own insurance might have "underinsured motorist" (UIM) coverage.  UIM coverage is required in many states.  Look at  your own policy and determine if you have UIM.  

If so, you need to get the other insurance's rejection on paper, and then forward it to your own insurance company.  

In best case, your insurance company would compensate you under UIM, minus your deducitble amount.  You can sue the other driver in small claim court to recover the deductible. 

If the "exclusion" is something else, please post the rejection email or letter.