well, I don't know fragmotion, but in general your description of what is happening isn't very detailed and is rather confusing. The picture has no real context and tells us little. This makes it such a broad question that it is difficult to even try to give you an answer.
if you are saying that when you move a bone, all connected bones move with it, do you mean both above it and below it in the heirarchy? if you are using forward kinematics, all bones parented to a bone *should* move with it, but not bones behind it in the chain. if you are using inverse kinematics, all the bones in the IK chain will move within their ability to meet your target position.
which bone is the base, and which are you moving, and which move with it? are you using forward kinematic or inverse?
also beyond the bone moving issues, it looks like you have some weighting issues. that bend in the blade for instance, it looks like it is getting pulled between weights towards the bone in the hilt and weights towards the bones in the fingers/hand, or perhaps they are not weighted at all and are in the starting position with only the hilt moving to cause the bend... a screen of the starting position and ending position as well as a description of the bone heirarchy would help us see what was happening better.
