Lin, I'm going to wait to mark it as solved because I'm one of those people that likes a consensus, if that's okay. I just want to see if anyone else chimes in. Plus, I really don't want it to be an invasive plant. I am so against invasives and that would let me unleash my full fury on it but I know how hard it is to manage other invasives. Skunk vine is the bane of my existence. I was sort of hoping this was native so I could at least think, "Well, it does belong here even if I don't want it right where it is." I also don't use many chemicals in my yard because I raise caterpillars but these things are very hard to get rid of so I may have to pull what I can and then do some selective application. Luckily, they're not really near my butterfly host plants so that will help.
Donald, unfortunately Florida (and other states, I'm sure) ended up with a lot of extremely invasive plants because someone thought it was "pretty" and didn't think about the fact that things just grow too darn well down here! We have a freeze warning tonight in the two counties directly north of me, but it often doesn't get cold enough to really kill things off like it would in other areas. For example, I was freaking out one time when visiting my grandparents in WV because nearly everyone had Castor Bean growing in their vegetable garden. I understand why, but here in FL it's an invasive plant and you find it growing on the side of the road because it doesn't get cold enough to kill it every year like it does up north.
Cheryl, the ones in the tree are way harder to get rid of than the ones in the ground. The roots are so much stronger than you would think. In the ground they're connected so you can kind of tug on one and get a bunch of others to come up sometimes. But the ones in the tree just end up breaking off their roots and then they come back. It doesn't help when they're spread by spores! It's not like I can get them before the seeds pods turn ripe like on other plants. And when I attached my bromeliad I cleaned out that tree first and tried to get rid of everything else in it. But as you can see, they keep coming back!