It is very common, and considered good medical practice, to do a second TURB. Often, during the first one, the urologist does not get enough tissue, or from the right place, for a complete diagnosis. The second time he/she knows exactly where and how deep the samples need to be taken. In my case, the first TURB showed papillary, low grade, tumors with some areas of irritation. The second, with special attention to the "irritative" areas, resulted in a diagnosis of CIS.
AND it is important to note that a definitive diagnosis of bladder cancer, as well as its grade and stage, CANNOT be made without the TURB and pathology reports.
If you and your father feel that a second opinion would be a good idea, and that you would feel more comfortable at a place with a lot of expertise in bladder cancer treatment, this would be a good time to make that move. You are fortunate that there are several excellent choices relatively close. You mentioned Memorial Sloan Kettering in NYC, There are also, a little farther away, Mass General in Boston, and Johns Hopkins in Baltimore. Of course you want to get this situation settled sooner rather than later, but a few weeks will not make a difference since this has probably been there for quite some time.
Should it come to a radical cystectomy (bladder removal) you would want him to be at a place that does LOTS of these. A neobladder is the most complicated surgery; when it works it can be a great option, but if it doesn't, not so much. And his age might complicate things. IF it comes to the point that he is considering bladder removal, there is a lot of information available. However, at this point, it might be "information overload."
Wishing you all the best
Sara Anne