I've just come across your post ... and whilst I'm no authority on ILR [being too early for my own wife to apply yet!] I share your concern. Two months does seem an *inordinate length of time to wait for confirmation of (what I believe to be of your "RIGHT" as a married couple who've lived here together for at least 2 years ... although *no doubt there are some who would disagree with me!).
Equally, I can understand your anxiety in needing to know the outcome asap, in the light of (hopefully) fulfilling your plans to attend your cousin's wedding in the US.
Doubtless, a visa WOULD be required.But there again, I could be wrong. And it's most likely someone else here will soon be able to advise you properly on that score ... although an alternative would be for you to contact the Home Office yourselves ...