I have posted a lot on this topic on the High Road. Search for posts by MillCreek on insurance. KingCreek, if you have the standard homeowner's umbrella liability policy, it likely does not provide coverage for self-defense/shooting incidents due to the 'intentional acts' exclusion. Shooting someone is an intentional act. You would possibly be better off arguing it was an accidental discharge, and therefore should be covered. Unfortunately, many appellate courts have ruled it is not, if you are pointing a gun at someone and it 'accidentally' goes off.
Many states, including Washington, have barred the sale of self-defense insurance, because it is not actually insurance in the legal sense, and does not have the necessary financial backing and other regulatory requirements. I do insurance and liability for a living, and I have never found it necessary to have this type of coverage, given that Washington actually has statutory law providing reimbursement by the state in these situations:
https://apps.leg.wa.gov/rcw/default.aspx?cite=9A.16.110
