Started picking at this Plumie and it looks worse than #1. Should I trim it or just toss it?

Yes, seems suffering more than the other one you have. I think it is done for seeing the core is looking like that already and the lower part nearest to the soil seems blackened.

But do inspect all the way down, uproot and check the part under the soil.

I agree with Tarev. It looks like a goner but un-pot it and see if there is anything viable (stem or roots).

Here is info about stem rot : http://www.plumeria101.com/pro...

Don't feel bad, just have to start anew, get a good cutting later when your overnight temps are stable and warm already. Thankfully it is Spring already, just a little more wait. Ken is a good source