It does have to do with the pronoun in your examples, but you can't generalize that.
The important question is: in your "dass"-clauses, who or what is the subject, and who or what is the object? The subject is in nominative, the object is in a different case, most of the time accusative or dative.
For your examples that means:
Meine Mutter findet, dass sie eine gute Ärztin hat.
I'm looking at the dass-sentence here and ignoring anything else:
Who/what has whom/what? She has a good doctor. So "she" is the subject, "eine gute Ärztin" is the object, that's why "sie" is nominative and "eine gute Ärztin" is accusative.
Der Mann sagt, dass er den Kaffee nicht mag.
Who/what doesn't like whom/what? He doesn't like the coffee. "Er" is the subject, "den Kaffee" is the object.
Susann findet, dass der Kaffee gut ist.
Who/what is good? The coffee is the subject here, that's why it's nominative.
People, things and pronouns can all be subjects or objects, it just depends on their role relative to the verb.
Der Mann sagt, dass seine Frau den Kaffee nicht mag.
Seine Frau mag den Kaffee nicht => "Seine Frau" is subject, "den Kaffee" is object.
Der Mann sagt, dass seine Frau ihn nicht mehr mag.
Seine Frau (subject, nominative) mag ihn (object, accusative) nicht mehr.