Hi. I know the underlined sentence means "Differentiating their izakaya restaurant from others is difficult.". And some say the bold に is a mistake, which should be が. Some say the に is a colloquialism to use -ni to introduce the aim of an endeavor for 大変だ, as in "最初はすごく理解されるのに大変だったけれど、"(I don't quite understand this explanation).
Could you please shed some light on the function of this に? Personally I don't really think it is a mistake, but I can't find this usage in my textbook ether.