In 1961, he was about to take up a post at the National and Kapodistrian University of Athens, but an intervention from the Palace deprived him of the opportunity. After King Paul's death, Peter found himself at odds with Paul's son and successor, King Constantine II. Had he not been deemed excluded from the line of succession due to his unsuitable marriage, Peter would have been heir presumptive to Constantine II according to the original laws of succession. However, the Parliament of Greece modified the Constitution to replace the original agnatic primogeniture with male-preference cognatic primogeniture, thereby introducing a number of female dynasts and their descendants into the line of succession. King Constantine II, still unmarried and childless, thus officially recognised his only unmarried sister, Princess Irene, as heir presumptive (excluding the older sister, Princess Sophia, who was due to become Queen of Spain). Peter remained convinced that the change was illegal and that he would be the rightful heir if the King died without fathering a son. Shortly after the King's marriage to their cousin, Princess Anne-Marie of Denmark, the uninvited Prince Peter called a press conference in Athens and openly questioned the legality of the constitutional amendment. Above all, he attacked his cousin Paul's widow, the tremendously unpopular Queen Frederika, and accused her of having a bad influence on her son. King Constantine II and Queen Anne-Marie's first child, Princess Alexia, was born in 1965 and designated as the new heir presumptive, but Peter refused to recognise that either. Following the rupture between King Constantine and Prime Minister Georgios Papandreou the same year, the Prince openly criticised the King's conduct and suggested himself as an alternative to Constantine II. However, the abolishment of the monarchy and the proclamation of the Third Hellenic Republic in 1973 did not allow Peter to fulfill his dream of ascending the Greek throne. After the monarchy was abolished, Prince Peter decided to liquidate his possessions in Greece, most notably his residence in Glyfada. From then on, he and his wife spent their time in London, Paris and Copenhagen. As the years passed by, their relationship deteriorated. They eventually decided to separate, but not officially. Ovtchinnikova moved to Hong Kong, while Peter took up a relationship with a young Englishwoman who lived with him in Copenhagen. Prince Peter continued to support the Tibetan cause. He was the president of the Nordic Council for Tibetan Assistance and was instrumental in helping Tibetans to Scandinavia in the 1960s. In 1967 he, "...was instrumental in procuring vocational training for young Tibetans in Denmark."