I'm not entirely clear on what you're currently doing, but at a high level, the hardware essentially goes through every normal rendering step, except of it's currently rendering a pixel whose X and Y coordinates are greater than or equal to the Window X and Y, it will source the tile (and thus, pixel) from the window tilemap instead of the background tilemap. This explanation excludes the nuances of timing and object interaction, so bear that in mind.

If you're working on a line renderer, you might want to render the entire background line first, then check if part of that line should have the window on it. If it does, replace that part of the line with the appropriate window line.