Imagawa lands in Kyushu were supposed to be due to a family relationship between the Ryzkoji (not sure on spelling) and the Imagawa clans. But... that's a different clan. XD Not Imagawa's. The Imagawa's were also related to the Hatekeyama and the Ashikaga I believe. But these clans were merely related, not working together. Maybe they just didn't want it to be too easy for Shimazu to take Kyushu.