No such thing as a stupid question, what might be stupid is doing something with out asking the question. What ever it is it is stressed and you aren't sure for 100% what it is. I wouldn't cut things up when they are stressed. Some corals/anemones will force themselves to split when they are stressed, but "fragging" them yourself will just add additional stress and probably kill it.
I wouldn't force it to split.
You could put it in your tank, but you would want to carefully acclimate it and something like this I would quarantine, but then again I quarantine everything and most people don't. Just my two gilders.
Edit(forgot I was back in the states): “Just my two cents.â€Â