Does homeowner insurance cover damages to a neighbor's home due to owners new construction or renovation or should we purchase a builders risk policy to be safe for demolition and rebuilding?

No, your home owners Policy does not cover damage by your contractor or builder. Always make sure that any contractor you hire is properly insured before you allow him to begin his work, If you are comencing self construction then by all means obtain a builders risk policy for coverage of incidental losses related to your construction activities.