Can the communications between Barbara and Amy be subpoenaed, or are they protected by Attorney-Client privilege?
The communications remain protected by the attorney-client privilege.
People Ex Rel. Herrera v. Stender, 212 Cal.App.4th 614 (2012) describes a pattern of unauthorized practice of law by a former lawyer who allegedly kept giving legal advice without informing his clients about his disbarment. The opinion nowhere suggests that their attorney-client privilege was invalidated or waived. Quite the contrary. For instance, the court reiterates the intent to "protect individuals in need of legal advice from seeking assistance from Martin R. Guajardo in the mistaken belief that he is a licensed attorney", Id. at 628. That intent is palpable also in the mention of "ad hoc measures from the court's equitable arsenal" to preserve the clients' privilege, Id. at 647, 650 (quotation marks omitted, brackets added).
See also In Re Grand Jury Proceedings, 219F.3d 175, 183 (2000):
[W]hen waiver occurs as a result of inadvertent [...] disclosure,
courts have limited the scope of that waiver based on the
circumstances involved and overall fairness.
(citations omitted). Your premise that Amy concealed her disbarment and made intentional misrepresentations about being authorized to practice law implies that Barbara's disclosures to Amy were inadvertent.
U.S. v. Warburg Pincus LLC, U.S. Dist. Court, Vermont (June 2022) reflects that "the attorney-client privilege can remain intact despite a one-time leak of privileged information" (citing cases). A multiplicity of communications between Amy and Barbara seems unlike to defeat Barbara's privilege as long as the premise of Barbara's [reasonable] unawareness holds.