We have an account that requires dual signatures on their checks. - how do we handle transferring from savings to checking or checking to savings. Also if one person comes in to cash CD's - does that also require dual signatures?

This is entirely a matter of your contract with the individuals or entities involved; there is no place to look up the answer except by reading your documents.

Many, if not most, banks will not accept accounts for individuals where two signatures are required. If they accept them for entities or organizations they require the entity to acknowledge that the "two signatures required" is only for the entity's internal use and that the bank accepts no responsibility for enforcing it.

As you are discovering, it's a pain and is not something you are obligated to agree to.