I need to split up facing page spreads so I can bleed into the gutter (the spine) without affecting the opposite page.

This is tricky, but can absolutely be done. The key is the Allow Pages to Shuffle option in the Pages palette flyout menu. There’s no way to split up a spread (or add pages to a spread) when this feature is turned on. However, if you turn it off, then you can have all kinds of fun….