You have some trans issues. I had the same whine you have in the transmission that I replaced (from my 1997 Lesabre 3800 series II). It'* definitely a transaxle whine from your description, it'* a common problem in the 4T60E automatics. There'* really no way to cure it except rebuilding or replacing the transmission. The factory actually has technical service bulletins describing the transaxle whine. The shuddering going up hill is most likely occurring in torque converter lockup mode. Either you have a misfire that is manifesting itself under this loaded condition, or you have (the also very common) 4T60E torque converter clutch shudder problems. I replaced my transmission at 70k miles due to shudder issues and burned fluid (and whine).