What version on MM sundance is it? spinning tail or bucking head? For bucking head, I know for a fact (I once took one apart) that it's not just a ball joint. the head is attached to the tail through some sturdy contraption encased in a plastic thing that runs through the body (same colour plastic as the body but harder. I guess same material as the "ball joint"?) for that version, you'd be best off pushing the short plugs inside the head and then using a reroot tool to root new ones in. as long as you don't tug on the hair it shouldn't come out again. Head removal only for this version I have not figured out how to manage.
For the 1st, front-legs-together-Sundance, I don't know what she looks like on the inside but my guess is again she's attached from the head to the tail. with some luck, it's some sort of rubber band contraption. Less luck, it's something similar to above, in which case I'd go with pushing the old plugs inside and just rooting on top of it.
Altho if you're feeling adventurous, I'd carefully see if head removal for this version was possible. (do in that case please keep us posted!)
good luck