The only way to attach corner to something other than the corner would be to use nulls and expressions. You would position the nulls on the corners of the screen then tie each null to the appropriate corner by calculating the difference between the position values of the null and the corner of the video. You would then move the nulls to the corner of the comp. I don't have the time to write the expression for you but if you are at all good at java math and expression language it shouldn't be too difficult.
Here's the problem with your idea, when you use corner pin like this you are effectively scaling up the image and the text and fine lines in a normal UI on a computer will quickly fall apart and look horrible. A better option would be to take a screenshot or a screen capture video of the computer screen and then attach that to the screen using corner pin. This would scale down the screen capture at the first part of the shot and then return it to 100% scale at the end. It will produce a much more believable composite. You may still have problems with fine lines and text as they are rendered to video but they will be a lot easier to manage.
Thanks Rick. Nulls and expressions would do the job. I'm a bit rusty but I think the expressions should be simple enough.
Thanks for your workflow suggestion. Unfortunately it wouldn't work in my case. It's a long story but it seems to pretty much work how I'm doing it. It was just dragging corners to align other points on the image is really fiddly and inaccurate.
I'll try the nulls method.