RewriteRule ^/some-old-url$ http\:\/\/www\.example\.com\/the\-new\-url [R=301,L]
The above rule will NEVER run because the leading slash will never match. Additionally, do not escape anything in the target URL. The target URL is literal.
RewriteRule ^some-old-url$ http://www.example.com/the-new-url [R=301,L]
This rule must appear near the beginning of the list of rules. The usual spot will be just after any rules that block specific malicious URL requests, and a long way before any index or non-www/www redirect.
What are the hosts "fixing" exactly? Sounds like they are adding rules to the main site configuration file that either contradict your htaccess rules or have syntax or other errors. If their rule uses Redirect or RedirectMatch then that is a big problem. Once you use RewriteRule for any of your rules you must use it for all of your rules.