Nancy,
In order to support Selenium Automation on Vivaldi browser, you would need to have a server component that is built using the
Selenium W3C specifications so that it can translate the Restful calls from the tests, into actions on the browser.
This server component would be similar to how IEDriverServer (for IE), ChromeDriver (for Chrome) and GeckoDriver (for Firefox) work.
Additionally you would also need a client library so that you can stuff like
RemoteWebDriver driver = new VivaldiDriver();
Selenium is moving towards a model wherein the Server component is basically built by the browser vendors themselves. If the server component is made available (I am not aware of the existence of one today), then it will be very easy for you to build the client component (viz., the VivaldiDriver).
So long story short, there is no way in which you can run your selenium test on Vivaldi browser [ not at-least to the best of my knowledge ]