While I was on probation in one county, I was arrested in another. So, I am on probation in two counties. I thought that the second county knew about the probation from the first one. Evidently, they didn't, and now the second county wants to arrest me for probation violation. Do I have any rights?

No more than any other person arrested and jailed awaiting trial has.

You can ask your lawyer.. because you need one ASAP. Maybe they can negotiate something favorable... before you get picked up under their terms...