2. Will the insurance company cover the homeowner.
Number 2 is what the insurance company will try to get out of. They will try to leverage any exclusions in the policy. If they can find an excuse not to cover the homeowner, they will get out or defend under reservation if rights while they try to get out.
Even if the insurance finds an out and does not cover the homeowner, the homeowner is still liable as is the dog owner.
Obviously lamas vary a bit by state, but this is generally true.
The OP should consult a personal injury attorney from a reputable law firm if they intend to sue.
These cases rarely make it to trial. They usually get settled.