A constitutional crisis would have been preferrable to such an assention.
Your protest is a difference without distinction:
as·sent
Noun
The expression of approval or agreement: “a loud murmur of assent”.
Verb
Express approval or agreement, typically officially: “Roosevelt assented to the agreement”.
There is indeed a distinction between 'assent' and 'approval', albeit a nice one (in the old sense of 'nice'). The constitutional position of the Queen on this was authoritatively set out by naturalman1975 in the course of some lengthy threads on the subject of the gay marriage legislation last week, and I have no wish to revisit that debate. But for the etymological, as distinct from the constitutional history of 'assent', and its gradual replacement in modern usage by 'consent', the full historical edition of the Oxford English Dictionary is instructive. The connotation of 'assent' has consistently been agreement that such-and-such a thing should happen, without the necessary implication that that thing is desirable or morally right: an implication which is, however, carried by 'approval'. The now rather old-fashioned notion of 'parental consent' to, say, a marriage, comes very close to this historical distinction. My daughter might persuade me to give my consent to her marriage with Mr X, but that wouldn't necessarily mean that I think Mr X would make a good husband or that it would be a happy marriage - implications which would be present if I gave my 'approval' to the marriage.
But when it comes to reflections on the Queen's character in relation to this action, the question whether she did or did not have a choice, to sign or not to sign, is rather beside the point. What is beyond doubt, for reasons lucidly set out by naturalman1975, is that she believed herself to have no choice, and that not to sign would have been a breach of her duty enshrined in her coronation oath. It's furthermore not in doubt that she would have received no advice to the contrary. That being the case, she cannot be personally criticised on moral grounds for taking what she believed to be an unavoidable action. Still less if, at the same time, she had also fulfilled her constitutional duty to advise and to warn, by warning in the strongest terms available to her of the grievous consequences of this Act. Since that advice and those warnings are only ever given in private to her Prime Minister, that can only be a matter of speculation: although I believe it to be highly probable.