Rewrite URL

Depending on how the remote site is configured you could create a node (pool member) for the remote site and use it as a pool member for the VIP for mylocalwebsite.com. This will allow clients to visit www.external.com while leaving mylocalwebsite.com in the address field.

However, in your example you're using a subfolder ("something") while you want to pull content from the root of the remote site. If this is required you can use HTTP::uri to rewrite the path. However, it would be much easier if you could use a subdomain (e.g. something.mylocalwebsite.com) instead of a subfolder, as that would eliminate the need to rewrite the request.