Princess Margaret never asked Parliament for its consent.
It had been made clear to the Queen that consent would not be forthcoming. The Royal Marriages Act states:
"Provided always, and be it enacted by the authority aforesaid, That in case any such descendant of the body of his late majesty King George the Second, being above the age of twenty-five years, shall persist in his or her resolution to contract a marriage disapproved of or dissented from, by the King, his heirs, or successors; that then such descendant, upon giving notice to the King's privy council, which notice is hereby directed to be entered in the books thereof, may, at any time from the expiration of twelve calendar months after such notice given to the privy council as aforesaid, contract such marriage; and his or her marriage with the person before proposed, and rejected, may be duly solemnized, without the previous consent of his Majesty, his heirs, or successors; and such marriage shall be good, as if this act had never been made, unless both houses of parliament shall, before the expiration of the said twelve months, expressly declare their disapprobation of such intended marriage."
http://www.heraldica.org/faqs/rma1772.html
The Marquess of Salisbury and other hard liners had made known their opposition to the marriage and their intention to resign from Parliament if it went ahead, so there was no point in her asking Parliament for its approval since she knew ahead of time that she wouldn't get it. I've also read that there was talk of putting a Bill of Renunciation before Parliament so that if Princess Margaret went through with the marriage she would have been required to give up her royal status legally. As it was, Parliament had already made clear that no Civil List income would be forthcoming after her marriage to Peter Townsend, which would have effectively prevented her from performing public duties.
Edward was NOT removed by the government over his choice of bride. They needed/wanted an excuse to get rid of him - her being divorced once and about to get a second divorce was a convenient excuse and the people would accept it. If he had been married to a suitable woman they would have come up with something else - he was a security risk at a time of heightened sensitivity in Europe - 1936.
Indeed. Meaning that if a person is considered unfit to be monarch, excuses will be found somewhere. In Edward's case, Mrs Simpson was the perfect excuse. In Charles's case, if enough powerful members of the Establishment are sufficiently concerned that he's too inclined to meddle in politics to be a politically neutral monarch or that he's too tainted by his actions and his statements regarding the Church to be a suitable Supreme Governor or that the Archbishop of Canterbury felt that he could not in good conscience go through with the coronation ceremony, then this remarriage might have provided a suitable excuse to suggest he step aside.
I think that if Diana had still been alive and Charles and Camilla had decided to marry, assuming Diana hadn't done something foolish PR-wise like marrying Dodi, there might have been quite a public outcry for the succession to skip to William under the guidance of his mother and to leave Charles and Camilla in a Duke-of-Windsor type of situation. Whether anything would have actually happened along those lines is a different matter altogether, but ultimately the existence of the monarchy does have to do with public acceptance of it, and they've been through some rough times over the past few years. The Establishment seems to be prepared to do what it takes to preserve the institution of monarchy even if that means being quite ruthless toward senior royals who are perceived to be a threat to the institution.
