I am a sunni (hanafi) by default and not by choice or rationale. I have developed a liking for my cousin. She is shi'i. Before pursuing any formal legitimate relationship I researched the differences between the two denominations in detail. I concluded that the shi'i and the sunni share the same basis of belief. It is only that some ahadith we accept and they reject. Contrarily, some other hadiths they accept which we reject. These differences have nothing to do with the religion itself. I seek your advice on that whether I should refrain pursuing my choice in front of my parents or take stand and try to convince them to help me. This may however, result in confrontation with my parents.
Legally the shi'i are Muslims and a shi'i woman can be taken into marriage. However, they differ greatly in the basic beliefs and a believer conscious about his/her personal faith and beliefs and that of the children should think a little before taking a shi'i woman into marriage. The difference between the shi'i and the mainstream Islam is not confined to views on a few contradicting hadiths. Mainstream Islam does not stand on the hadith narratives. The basic beliefs and practices are founded on the Qur'an and the Sunnah. By Sunnah is meant the religious practices like prayer, hajj, zakah, sawm, marriage and birth rites and other such practices which have been taught by the Prophet (sws) to the entire generation of the Companions (sw) who then passed them on with their consensus to the next generation. Thus these practices have reached us through perpetual adherence of all the believers in all the layers of the Muslim generations. This makes them absolutely authentic like the Holy Qur'an.
The Shi'i also believe in the institution of Imams regarding whom they consider almost equal to the Prophet (sws). We on the contrary believe that the agency of prophethood has been closed with the Prophet Muhammad (sws). (for detail about the Shi'i belief on imamat please refer to the following discussions: http://al-mawrid.org/pages/questions_english_detail.php?qid=9&cid=374&search=imam, http://al-mawrid.org/pages/questions_english_detail.php?qid=17&cid=374&search=imam, and http://al-mawrid.org/pages/questions_english_detail.php?qid=153&cid=374&search=imam.) This is the only difference between the two that puts them completely apart.
Then there is the social problem. If your parents do not approve of this marriage or her parents resist then it would create problems for your family life. Please note that it is only the recognition of the family and the society that helps a marriage work. We can no doubt marry a person of our choice against the will the parents and the family but by doing so we incur a great cost. We may not find the help of the family in future and it may render it very difficult for us to make the marriage work smoothly. Therefore you should try to convince your parents and seek their help and support before you marry the girl.
May God help you reach a wise decision and make your union a happy and lasting one if you decide to go with your decision.