My impression is that Kitty had no difficulties in the US other than not being born rich. It occurred to me just now to wonder how she managed to get a job as governess for the Earl of Hampshire's children: I'm surprised that the Earl hired an American governess. She must have had very good references. Maybe she faked them.
As for whether or not she and the Earl had a good marriage, she claims it was happy, and Edward believes it was happy, but there was a lot that Kitty didn't tell, and Edward would surely view the British aristocracy through rose-colored spectacles. I don't think we ever got the full story of how Gerald ended up in jail, and I can't remember clearly what we did get, but my impression was that Kitty was somehow involved.
But as Kitty was planning to marry Edward for the money she believed him to have, she wrote to her mother, "Edward is a dear," and I don't think she would have married into a situation that would have been too uncomfortable for her. So probably her marriage to Gerald started out happy enough.
One thing that bothers me is that Kitty apparently didn't know the financial setup at Collinwood. At the time when she was pursuing Edward, Trask was touting herself as Master of Collinwood. That should have tipped her off to the fact that Edward didn't have much money, but maybe she was too distracted by the problem with Josette to notice. Or else she may have decided that it was worth marrying Edward even without the Collins fortune, because living at Collinwood would be a nice, secure berth, but if mere security was her goal, I would expect her to aim for a husband in Boston or New York rather than in the wilds of Maine.