Peter Anderson5 wrote:
2015 MacBook Pro 13" running 10.11.4, Safari 9.1
Apple TV Model A1625 (64GB) running 9.2 software
What device creates your network? It is either an Apple AirPort Base Station (Extreme, Express, or Time Capsule) or some other manufacturer's product.
If you are using any so-called "anti-virus", "Internet security" or "firewall" products on that MBP, remove them according to their respective instructions. Do not reinstall them regardless of the outcome.
If you did not install anything resembling that description, contact AppleCare. The problems you're describing are bizarre.