I have a suggestion that bypasses the problem altogether. (Generally speaking, if something looks strange, even if it's technically correct, you should rephrase it.)
I'm glad he didn't see me in a Harrow class.
In this case, Harrow acts an an adjective. Just as does math in I'm glad he didn't see me in a math class.
There is no need to use the nickname. Also, if you did use the nickname, you could not say in a The Harrows class, and would have to rephrase it:
I'm glad he didn't see me in a class taught by The Harrows.
In response to "Which one?", you would clarify, "Oh, I mean Phil Harrow," or, "Either one.")
If you really want to keep the possessive form of the original sentence there is only one way of doing so:
I'm glad he didn't see me in Phil Harrow's class or Zoe Harrow's class.
You can also consider a simpler example that has fewer issues.
There are two professors, A. Smith and J. Smith. The following is perfectly correct but leads to ambiguity:
"I'm glad he didn't see me in Smith's class."
In actuality, to avoid ambiguity, you would say:
I"m glad he didn't see me in A. Smith's class or J. Smith's class.
Or, you could rephrase it as I did the original problem:
I'm glad he didn't see me in a Smith class.
What you would not do is use a possessive form of a plural:
I'm glad he didn't see me in (one of) the Smiths' classes.
It's wrong, because it implies joint ownership. They don't both teach the same class. If this simplified version is wrong, then it needs to be rephrased. This is no different from the more complex version—it's just that the more complex version misleads with other considerations.