Answer

For the tsm commands to pass the .json file to server and apply pending changes, please see: web-data-connector-settings Entity

To create a .json file with multiple WDC and secondary URLs, please see the following template:
 

{
  "configEntities": {
    "web-data-connector-settings": {
      "_type": "webDataConnectorSettingsType",
      "refreshEnabled": true,
      "whitelist": {
        "https://www.mysite.com:443/wdc": {
          "secondaryWhitelist": ["https://www.mysite.com/.*", "https://www.coolapi.com/.*"]
        },
        "https://tableau.example.com:443": {
          "secondaryWhitelist": ["https://tableau.example.com/.*"]
        }
      },
      "enabled": true
    }
  }
}

Copy/paste the template into Notepad, and replace the listed URLs with the actual WDC URLs and secondary URLs needed for whitelisting. Please note that secondary URLs must be separated by parenthesis and comma, as shown above. Additionally, the two WDC are separated by a comma after the immediately-following curly bracket. Ensure that you save the Notepad file as .json.
 

Additional Information

1. The primary URLs need to include the port or this won't work.
2. An * does not work for wildcards, it needs to be .*
3. The secondary whitelist needs to be an actual array not a concatenated string