Under Colorado law, you have several options to consider for recovering the $3,000 deductible you had to pay due to the home inspector's negligence. Given that the amount in question is $6,000, this falls well within the jurisdictional limit for small claims court in Colorado, which is $7,500. Filing a case in small claims court is generally quicker and less expensive than going through a full civil court process. You can review the instructions and forms on the Colorado court's website. You would want to sue for the full amount of damages, not just the deductible. You will have to reimburse your carrier the $3,000 it spent if you were able to win and recover the $6,000.
Another option it is try to get your insurance carrier to help. Since your insurance company covered the initial damage, they may have a subrogation right to recover the amount they paid from the responsible party. Consult with them to see if they can pursue the inspector's insurance company on your behalf. Since the inspector likely has insurance this may be a viable path to recovering your damages, which has the added benefit of the insurance carrier doing the work for you.
Finally, the buyer could possibly be liable in this situation under the purchase agreement (unlikely if Colorado's form purchase agreement was used), a theory of negligent hiring, or possibly an agency theory. Given the total damages it would probably not be worth the effort given it is unlikely you would prevail against the buyer.
Good luck. I agree your offer to pay 50% of the deductible was a generous one.