There may actually be a bug in Poser... I have to run another test to be sure, but the massage chair that I created did the same thing. Granted it's a lot more complicated than a 3 part mushroom, but I did everything right:

1. I grouped it in Wings

2. imported into Poser

3. went into the group editor and spawned props

4.hierarchy editor and parented parts, selected the main parent, created a new figure....

BAM

When I loaded it onto the stage, there was only a couple parts there.

I am going to redo it later on today (it's 7:45 am here in the Philippines) after I have my coffee and I will post the results.

If I get the same thing 2 times in a row, I will put a ticket in with SM...

If I had a nickle for ever time a woman told me to get lost, I could buy Manhattan.