Unless one of those 2 ADSL routers can have the ADSL portion disabled so it will act as a pure Access Point, you will have a problem trying to connect them to just one broadband connection.
You can connect an Access Point device to an ADSL router.
So for example;
ADSL router connects to your existing 7 computers, and a Device acting as an Access Point.
The 10 PCs can then connect to the Access Point.
I hope they already come with ethernet connections to save your charity the costs of buying ethernet cards, and you the hassle of fitting and troubleshooting any installation issues!
Not too sure, but I think the 10 PCs can be setup as a separate workgroup to your existing 7 PCs which will prevent access?