Tree from our front yard damaged neighbor's garage

Our neighbor informed us that a root from a tree in our front yard has intruded into her garage floor, and that here elderly relative tripped while walking in the garage. She is doing a claim on her homeowners insurance to have it repaired, and has communicated that her insurance will eventually try to collect from our homeowners insurance. What are our obligations in regards to the damage to the garage and to the injury of her relative? Also, she is having the root removed which most likely will kill the tree, so will having the tree removed be our full responsibility? Its a very large, old, and pretty tree that provides a lot of shade during hot summer months, but if it becomes a major hassle, we would prefer to have it removed to keep the peace. We're trying to understand our obligations to see if we can pay this out of pocket to avoid our rates going up.

Location: Colorado