Hi, the web user interface is not hosted on CORE2 board, but on cloud.husarion.com. Even if you create a web UI that is hosted on your laptop it will still need to have access to cloud.husarion.com to control your CORE2. It doesn’t matter whether your CORE2 is in the same network or not.
CORE2-ROS gives you more capabilities in controlling through local network than CORE2. You can “upgrade” your CORE2 to CORE2-ROS by replaceing ESP32 Wi-Fi module with a Raspberry Pi 3 (or ASUS Tinker Board) working on system image that you can find here: https://husarion.com/downloads/ . The physical connector is different, so some cables soldering would be necessary.
But if you achieve to do that, you will be able to host your web UI on CORE2-ROS and to access that from your local network.
If you need to have a local connection to CORE2 and CORE2-ROS is not fine for your project, consider using a bluetooth module that you can connect to hExt or hSensor port and write your own desktop or mobile app to access your device.
If you will have any further questions don’t hesitate to ask