Keyframes are going nuts in after effects and premiere

There is a difference between temporal interpolation and spatial interpolation. When you get a layer moving then you stop it, then you set another keyframe a couple of frames later and start it moving again the velocity of the incoming motion will continue after the second keyframe then the layer will bounce back into position. When it leaves that position after the third keyframe it may start moving in the opposite direction before it moves forward again on its way to the fourth keyframe. This is called Ping Pong. If you select the layer and have keyframes visible you should be able to see the bezier handles in the timeline that shows you the motion path. You can fix this problem with the Pen tool or by clicking on a keyframe and changing the Spatial Interpolation to Linear. There is also a setting in the Preferences/General tab to change the default behavior. Linear is not the default because it usually doesn't look very good. Once you get the hang of it, and once you learn how to use hold keyframes, this problem goes away.