As for the Sunni claim that a wife by Mut'a is not a...

As for the Sunni claim that a wife by Mut'a is not a legitimate wife because she does not fulfill the religious requirements for being a 'wife', this also is false. In the question of inheritance, the Quranic verse is a general one, and there is no reason to suppose that it may not have certain exceptions. In fact, the specific requirements of Mut'a as established by the Hadith literature show that Mut'a is an exception.

Nor is it the only exception, since a non-Muslim cannot inherit from a Muslim, nor can a murderer inherit from his victim. Also if a man is sick and marries a woman, but dies due to that sickness before consummating the marriage, the woman will not inherit from his husband. Thus being husband and wife (even in the permanent marriage) does not always necessitate the inheritance.

Quran usually provides the general rules and he was the Messenger of Allah who clarified the exceptions as well as the conditions for applying the rule. In short, inheritance pertains to permanent marriage, but even in permanent marriage it has certain exceptions, so that the verse establishing it cannot be interpreted as nullifying the validity of Mut'a. Also inheritance is possible in the temporary marriage as long as it is made condition at the time of contract.

(See Asl al-Shia wa Usuliha, by Kashif al-Ghita', p116; al-Bayan Fi Tafsir al-Quran, by al-Khoei, p219) In the question of the child, there is no reason to claim that it is illegitimate. In Mut'a the "bed" is legitimate, so is the offspring. (Sharh al-Lum'a, v5, p277) The Imam Ja'far was asked: "If the wife becomes pregnant as a result of Mut'a, to whom does the child belong?" He replied: "To the father," i.e., the child is legitimate.

(Wasa'il al-Shia, v14, p488) In a similar manner numerous traditions exist to prove that a wife by Mut'a must observe the waiting period of two months. Some of such traditions are even documented in the Sunni sources.