Taking into account that your client doesn't want to change companies for whatever reason, I will offer a few ideas to help the agent capture her leads. Our local MLS doesn't allow individual agents to use their own IDX if the broker has it on their site, so we are in the same boat of having to frame it through no fault of our broker.
My broker got a completely new site in February and the set up now is such that the page I frame is identifiable as "mine" so the leads which come through it are also mine.
Before that, though, I had to do whatever I could to capture the leads rather than having them go through the broker's system. I tried a couple of different things with varying degrees of success.
1. Require registration to search. When visitors click on "Search" they are first taken to the registration form. You get lots of registrations this way, but many others will just go away mad.
2. Put a brief form in the left frame of the page which requires name and contact info and space to put MLS numbers for more info or showing requests. This will result in fewer leads, but they will be more serious and less insulted by the registration process.
Good luck,
CiCi