Hi!
I'm not sure what you mean by "unable to change position". Do your controls not move at all, when you use the move or rotate tool on them? Or do they snap back in the previous position after you move them?
Also there are 2 things in your comment that are already things that are not normally done during animation:
1) If you have joints that are already connected to controls, you don't keyframe the joints themselves. Because if those joints are connected via Parent constraint, you will create a conflicting control hierarchy between the animation curve on the joint and the control. This could be the cause of your issue.
2) While animating. the frame you want to key on is normally not selected by using the shift key, but by simply clicking on the frame you want your keyframe to be on, the gray square that indicates where on your timeline you are will automatically jump to the clicked frame. Shift selecting frames is usually done to take an existing frame or multiple frames and move ist somewhere else in the timeline.
Also, if you are able to change the position and they jump back into the previous one, you probably did not keyframe your second position (hit the S key after positioning it), which is something you have to do for every keyframe unless you got "Auto Key" toggled on (small square on the right side of your timeline, right next to the timeline settings)
I hope this helps!
