I think it may be easier than you think.
Let me use an example. Let's say everything is working OK before adding the ppa on one of the laptops, and that you want to install the package 'mediainfo' from here 'ppa:shiki/mediainfo'.
In one laptop, you add the ppa to its sources:
In order to let apt-proxy-ng to cache the sources' index files, you simply just update:
sudo add-apt-repository ppa:shiki/mediainfo
That would get the index files cached on the server.
sudo apt-get update
Then you can install the application:
That would also cache the package on the server.
sudo apt-get install mediainfo
If you want to install it on the other laptop, you follow the exact same procedure. The difference will be that the index files and the package itself have been cached, thus it will be very fast, and you'll be saving bandwidth.
I hope that helps. Let us know how it goes.