Track matte not working as expected

Hello folks. I am dealing to get something very specific with track matte but I don't know how to do it. I guess it is not imposible to achieve so most probably I am missing some steps as the results shown is not what I need. 

I want to see a video inside a "glass window with curtains and frames" while there is another video in background. 

Video for background is in V1, video for inside the window is in V2 and the window is in V3. 

The window is a still image. I have two versions for the "glass", one being white and the other being transparent. The frames are black and around the window there is a frame white and another frame pink. There are pink curtains holding from the top. 

What I need is to see the V2 video only inside the "four glasses" without losing the curtains and the window frames including the + inside. 

This is what I did: I drag track matte in V2 and assign it to V3. I get the effect but not as expected because I don't see the frames and the curtains. With alpha the pink and white around the corner dissapear and the black frames show me the V1 video. 

Any idea about how can I get the V2 video showing just inside the window without losing the black frames and pink curtains? 

Thank you for your help