How do you tell my local server to interpret all relative pathways, that begin with a /uploads/, from the remote server (the development server)?

The uploads folder has run out of version control and that i do not have it during my local server (the testing server).

You should use the mod_proxy module of apache.

ProxyRequests Off

<Proxy *>
  Order deny,allow
  Allow from all
</Proxy>

ProxyPass /uploads http://live.domain.com/uploads
ProxyPassReverse /uploads http://live.domain.com/uploads

The ProxyRequests Off hinders forward proxy so that your machine can't be utilized for a proxy server.

The <Proxy *>...</Proxy> sets the access privileges for your (Reverse-)Proxy 'all' within this situation.

And finaly the ProxyPass and ProxyPassReverse define that each request to '/uploads' ought to be passed onto 'http://live.domain.com/uploads' (->ProxyPass) and each response from 'http://live.domain.com/uploads' ought to be treated as it might be from '/uploads' (->ProxyPassReverse).