Labor is not olmert's party which is Kadima. The two of them are the main components for the ruling coalition.
Peretz is Labor. The authentic headline for this article is, "Laborites slam Peretz for supporting talks with Syria." The headline does not make the stunning but demonstrably false claim that you do, namely that Olmert's coalition is falling apart. Rather, the headline indicates dissatisfaction among Labor Party members with the party's own leader.
There is no information in the article, as I read it, that supports your claim that Olmert's coalition is falling apart.
Moreover, by putting a made-up headline on the article you are violating Free Republic procedures and making it difficult for anyone to find this thread in the future by searching for it by its genuine headline.