The Splash Page was designed to be a placeholder for the gallery in Small Screen Mode (essentially an image link with some information) where the gallery may be too small to be useable (on small screen devices) if it is embedded into a web page. When the Splash Page is clicked (or tapped), the gallery is expanded to give the images as much room to be displayed as possible.
You can still use the Splash Page in Large Screen Mode if you like (by setting showSplashPage="ALWAYS") but the Splash Page's functionality will remain the same.
There is a little more information about the Splash Page in the Screen Modes section of the Gallery Tour.
There is no way to override how the Splash Page functions in a Juicebox gallery and it sounds like you might need to create your own custom version of the Splash Page in your web page and load your gallery in its place when it is clicked.
This would certainly be possible but knowledge of HTML, CSS and JavaScript will likely be required (and it would be much easier to work with the available configuration options to reach a compromise).