Yes, that IF in that statement is the big hurdle.... and that IF is really at the center of much of the rest of the issue. Who has the "right" to enforce their view of the greatest happiness of the greatest number on everyone else who disagrees?
As I have mentioned before, that IF rests on education, opinion, and various, loose supporting evidence (such as people are social creatures, people tend to be happier when they work together, etc.). It comes down to an abstract ideal which can be accepted, rejected, or anywhere in-between by an individual.
One could ask, who has "right" to enforce any philosophy and what does that mean? Utilitarianism states laws are meant to promote total happiness; what gives police/government the "right" to enforce laws? I think this is a discussion which applies to far more than just utilitarianism.
If you mean silencing others, know that Utilitarianism is very strong about maintaining freedom of speech. John Stuart Mill's On Liberty focuses greatly on that.
"Truth gains more even by the errors of one who, with due study and preparation, thinks for himself, than by the true opinions of those who only hold them because they do not suffer themselves to think. Not that it is solely, or chiefly, to form great thinkers, that freedom of thinking is required." - John Stuart Mill, On Liberty, Chapter 2
"First, if any opinion is compelled to silence, that opinion may, for aught we can certainly know, be true. To deny this is to assume our own infallibility. Secondly, though the silenced opinion be an error, it may, and very commonly does, contain a portion of truth; and since the general or prevailing opinion on any object is rarely or never the whole truth, it is only by the collision of adverse opinions that the remainder of the truth has any chance of being supplied." - John Stuart Mill, On Liberty, Chapter 2
I believe the Epicurean answer to the greatest happiness for the greatest number is to get more people to follow Epicureanism
Doesn't every philosophy, religion, and belief systems more or less hold that everyone would be "better off" if more people followed their beliefs?
Convincing, not compelling, people is crucial to truly making their lives better. If they honestly believe in something, they will more likely and more greatly follow, support, and benefit from it.