But in the 20th century, or even the 1880s when they married, money was a better ticket to access power than blood.

Not really. That might have been the case in America but in nineteenth century Britain - even the late nineteenth century - money could take you only so far. Cora and her family may have had business interests they wanted to further in Britain but found that they quickly hit the social barriers of being (i) foreign and (ii) commoners. English aristocracy were (and still are, what's left of them) a very insular lot, and they still dominated politics at this time.