The main problem is that you let this situation happen 
You should have broken down the Uesugi a long time ago. My advice: try to get Yamans in on a war with you against Uesugi. Then try to get one of the Uesugi province that borders Yamana. You can now try to set up a plot with Shimazu to attack the Yamana. After taking a few province from Uesugi, peace out with them and let them fight only Yamana. Then spring your plot against Yamana.
You should have broken down the Uesugi a long time ago. My advice: try to get Yamans in on a war with you against Uesugi. Then try to get one of the Uesugi province that borders Yamana. You can now try to set up a plot with Shimazu to attack the Yamana. After taking a few province from Uesugi, peace out with them and let them fight only Yamana. Then spring your plot against Yamana.