All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
There is no doubt that a woman's Diyyah (blood money) is half of that of a man; there is a consensus amongst the scholars on this issue.
It is not permissible for this ruling to be objected to or rejected by the parliament. Rather, the parliament must fulfill and execute the command of Allah, and act according to the rulings of His Sharee’ah.
Every Muslim must submit himself/herself to the Ruling of Allah whether or not he knows the wisdom behind it. Allah Says (what means):
• {It is not for a believing man or a believing woman, when Allah and His Messenger have decided a matter, that they should [thereafter] have any choice about their affair. And whoever disobeys Allah and His Messenger has certainly strayed into clear error.} [Quran 33:36]
• {But no, by your Lord, they will not [truly] believe until they make you, [O Muhammad], judge concerning that over which they dispute among themselves and then find within themselves no discomfort from what you have judged and submit in [full, willing] submission.} [Quran 4:65]
It is acceptable for a believer to try to know the wisdom, because knowing it increases his certainty and reassures him. Some scholars stated the wisdom of making a woman's Diyyah half of that of a man. Ibn Al-Qayyim said in his book I’laam Al-Muwaqqi’een:
"With regard to the Diyyah (blood money); a woman is more deficient and lacking than a man, and the man is more useful than her. A man occupies positions that a woman cannot, such as religious posts, positions of authority, safeguarding the frontiers of the country (from being attacked by the enemy), performing Jihaad, and doing crafts that are indispensable for the interests of the world, and defending the religion and the worldly matters. Therefore, their Diyyah is not equal, because of all this [..] Hence the wisdom of the Law Maker (Allah) necessitated that her Diyyah is half of that of a man, because of the differences between them." [End of quote]
The fact that the man's Diyyah is greater than the woman’s one is, undoubtedly, in the interest of the woman, as pointed out by Shaykh Mueen Ad-Deen (as you mentioned), because the woman will inherit a greater share than if the Diyyah (of the man) was a half, as in the case of a woman's Diyyah.
As for your question about whether the wife gets the whole Diyyah, then the answer is no. The Diyyah is divided among the heirs Islamically, including the wife –if there is no impediment that prevents her from the inheritance. Therefore, she takes her share from the Diyyah, which is either one-eighth if her dead husband has inheriting children, or one-fourth, if her husband has no children to inherit him.
However, it is not necessarily that the heir of the Diyyah be the wife; it may be that the heir is one daughter, so she takes half of the Diyyah. It may also be two or more daughters, in which case, they take two-thirds, and so on, according to the shares assigned in the Sharee’ah.
Allah knows best.