I really happy I decided to reread the series after I read TGS. I have what may be the answer to the questions why only 4 clans went to punish Laman.

From The Shadow Rising. Seana was talking about Rand's father Janduin.

"He was clan chief of the Taardad, then, the youngest in memory. Yet he had a way to him, a power. People listeded to him, and would follow him, even those not of his clan. He ended the blood feud between Taardad and Nakai after two hundred years, and made alliance not only with Nakai, but the Reyn, and the reyn were not far short of blood feud. He very nearly ended the feud between Shaarad and Goshien, as well, and might have had Laman no cut down the Tree. Young as he was, it was he who led the Taardad and Nakai, the Reyn and Shaarad, to seek Laman's bloodprice."

The four clans who followed Janduin, the leader of the Aiel seeking Laman's bloodprice, were allied with the Taardad or had really good relations with the Janduin.