Thanks, HBorre & Wolf.

I'm only using IK because you have to have that on to parent a hand to another object, as far as I know. If there is a way to parent without IK that might work, but the only non-IK parenting I'm aware of is parenting a whole figure.

Wolf, I did try that, and it works to parent Figure 1 to a ball on Figure 2, but unfortunately once you do the same thing with Figure 2 to figure 1, you get the same problem. I guess it seems like Poser can deal with one figure holding to another, but not both figures holding to each other.