Actually an MD is a medical doctor and can prescribe meds, as well as a Nurse Practitioner. PhDs cannot are not medical doctors - I work for one and among many . Some super ambitious ones are MD's along with a Phd and they do clinical work with research. The PhDs just have more research based experience. With a PsyD, the extra experience is clinically based. So there is an advantage to a PsyD, I get the bias (and I'm studying for my Counseling Masters). It all comes down to hours of Post Masters experience and hours of supervision.

There see many excellent LMHC's out there but for a case like yours I understand not wanting to work with an inexperienced one. But in all fairness, the next level down from a doctorate in terms of clinical experience would be an LICSW (not an LCSW). That "I" in the license title is earned by working under supervision for a lot of hours. So these therapists are not newbies and can handle complex cases. I wouldn't shut them out of consideration. It's worth the effort since the PsyD you have now sounds like she has issues of her own.