Yes, a doctor may refuse to examine you for or give you a second opinion: you may have a right to seek one, but that does not require any particular or individual doctor to see you. You need to find a doctor who will willingly do this; doctors are allowed to decide who to see, and who not to see, as patients. If this other doctor wants to not see you as a professional courtesy to the 1st doctor, to avoid conflict, because they only see their established patients, etc., that is their right.