That first sentence is a doozy, but if you can re-arrange the "to [Recruiter Company Name]" so that it comes at the end of the sentence instead of the beginning, then you can add your "on site" stipulation at the end.
Then it would read something like the following.
"The Supplier hereby assigns all existing and future Intellectual Property Rights in the Services and the Inventions and all materials embodying these rights to the fullest extent permitted by law to [Recruiter Company Name] for only those Services, Inventions, and materials produced at the business establishment ("on-site") of [Recruiter Company Name]."
It wouldn't hurt to add another sentence as well to make it clear that you will retain rights of authorship and ownership of code that you write outside work.
Something like, "Furthermore, The Supplier retains all rights of ownership and authorship of materials which are not produced at the business establishment ("not on-site") of [Recruiter Company Name]."
The most important thing in contracts is clarity. So be explicit and make clear what you are looking for in the contract, and that the contract contains the wording to your satisfaction.