Suppose a contract exists in which defendant D has indemnified party E. D and E currently dislike each other. Third-party plaintiff P, in a liability matter arising (indirectly) out of the contract, has sued defendant D. He could have chosen to sue E in addition to or instead of D, but he didn't; only D.
D requires documents from E in order to prepare the defense. But party E, out of spite, refuses to provide them. D does not want to have to subpoena E, because it would reveal to the plaintiff that D and E are not on good terms; moreover, the plaintiff has not brought E into the case at all and D would rather just keep them out of it entirely.
Does D have any other recourse against E in this matter? Does this possibly constitute bad faith on the part of E?