I think you should review your contact first. It is very tricky and risky if you rent your house to someone without a well-defined lease or contact. I believe your tenant might find something she could take advantage of it. Normally, this kind of agreement will have location describing the tenant has inespected the house and feel fully satisfied to move in. That means she could not complain the premises if there is nothing to be repaired or fixed. If you both signed the lease, you could not relase without the permission of other party.
On the other hand, lanlord should have the responsibility to provide the tenant a comfortable living environment. If I could catch a mouse in this house, I would feel scared too. My opinon is to get someone to walk though those details with your tenant, and confirm them one by one as a record. Based on the confirmed list, you two could negotiate a new price or keep the original one with / without fixing.
About the insurance, you don't have to show the policy to your tenant, but you have to clarify whose responsibility right now. In my opinion, it should be yours, so you need find a way to eliminate her concerns, either adding some support or find a contract to duble check with a written record to eleiminate the cocernes from your tenant, and double check with your insurance company.
You are in business, and customer satisfaction is important, no need to be emotional, even that is a sensitive tenant, it is just your luck.
