Hmm...

I wonder if they are actually rivets? You might try searching for methods to remove rivets - I just did a quick search and there are a ton of ways to do it, but without seeing your toy, not really sure which one would be best.. Another thought I have is if the "screw" you have is actually screwed in.. in that case, you might be able to get a pair of needle nose pliers on opposite sides of it and twist counterclock-wise like a regular screw..

My guess is that's its a rivet, tho..

Regarding the plastic base.. if you can just get the dang thing out, you can always replace it with a larger screw and "dig" that into the plastic to hold it in place - or depending upon how thick the plastic is, you could fill the hole with either elmer's glue, or wood putty or silicone or something to give the new screw something to dig into..

I'll try to look up your toy and see if I can get any other ideas.. Right now, I'd start with removing a rivet..

---

Friendship is like peeing your pants.. Everybody can see it, but only you can feel the warmth..