Transmission trouble

The inner CV joint on the passenger is wobbling to the point that it makes the car body shake at speeds of 80 to 100kph. Last week I removed the axle and tried to touch with the finger the splines inside the trans. Splines were ok, but the part having the splines were moving left and right using just my fingers. Somebody said movement in the differential is normal. Well today, I helped a friend change the outer CV joint of his 97 civic so I took the opportunity to peek inside his trans. The part having the internal splines have very little horizontal movement compared to mine. Now Im sure the problem is inside the trans. IS there an easy way to repair/ replace the damaged part. Can it be done without taking off the whole trans down? I cannot remove a trans alone. My workshop is under a tree along the road. Pls help!