Why do Shi'as allow mut'ah marriage?

According to Sunnis, mut'ah (temporary marriage) was allowed before but later the Prophet salallahu alayhi wassalam abolished it. It is based on the following hadiths (traditions): > In the Two Sahihs, it is recorded that the Leader of the Faithful `Ali > bin Abi Talib said, "The Messenger of Allah prohibited Mut'ah marriage > and eating the meat of domesticated donkeys on the day of Khaybar > (battle).'' In addition, in his Sahih, Muslim recorded that Ar-Rabi' bin Sabrah bin Ma'bad Al-Juhani said that his father said that he accompanied the Messenger of Allah during the conquest of Makkah, and that the Prophet said, > O people! I allowed you the Mut'ah marriage with women before. Now, > Allah has prohibited it until the Day of Resurrection. Therefore, > anyone who has any women in Mut`ah, let him let them go, and do not > take anything from what you have given them. What is the evidence that the Shia used to allow it? Are there any conditions to perform Mut'ah ? What happens to the woman and her children after the Mut'ah marriage ends?