my daughters car gets a wobble in front end had tires checked and balanced. undercar on left axcle looks like some kind of round balancer or something, it is loose and moves back and forth on axcle is it spose to be this way. if not where should it be positioned

 

That is called a Dynamic Dampener, and no its not supposed to be lose. You probably should have that half axle replaced.
If its been doing it a while, I would check the wheel bearing and the spline seal on the transmission as well while the axle out for damage and leaks.