'Stitching' together cropped videos software

Hi Guys,
Apologies if this is the wrong forum.
Does anyone know of any video editing software where you can do either what's in the description or where I can crop one area from one video then overlay it on another video. Specifically what I want to do is create logoless BBC TWO idents using 2 videos of the same idents used with the 50th box logo and the centralised BBC TWO NI logo. I want to crop the area on the right hand side of the video where there is no logo then paste it over the 50th ident video so there is no logo visible at all. I'd be happy to share what I create, giving full credit, of course to the original sources of the videos/clean music.
Thanks 😀

What editing software do you have access to?

I would personally recommend Sony Vegas' masking tool.

I currently have windows movie maker and I've been using 'remove logo now' so far to try and blur/mask box logos, but that's not always an ideal outcome.

Thanks for the tip about Sony Vegas Caven

I use Adobe Premiere, so I would've laid the two clips on top of each other and used Crop to mask.