A year ago, I said this wouldn't work. However, I recently tried it and it works, although I'm not saying it would work perfectly every time. The trick is to set campaign #2 with lower bids. The idea is that the Google-only campaign would trigger more often while the search partners campaign would trigger mostly on the search partners.
You are competing against yourself in a way. There is no way to trigger campaign #2 100% of the time on the search partners only. But if you get 90% of the time, I think that's acceptable, even 80% would be.