By inviting Batwoman in as a member of Batman, Inc. Batman is essentially attempting to instill his control over Batwoman and her operations. Not only would the heroine no longer work alone, but each and every one of her moves would be documented. Kate knew this, which may be part of the reason why she refused the offer. This might also be the reason why when confronted with an invitation by the D.E.O. she rather willingly obliged.
Really? You don't think the D.E.O. threatening to have her father court martialed and thrown in prison had anything to do with it?