Woody wasn't upset with Hope for revealing that information or anything, he was upset because he gave the haters something to latch on to (something to give legitimacy to their trolling/hate/etc.).

Many people use their kids to make money. Parents own a restaurant... would it be wrong for the parents to ask their kids to help clean up the restaurant after school or something? My best friend's parents owned a restaurant that he worked at in his spare time (without pay), and I think his parents are awesome and so does he. Would it be wrong for a farmer to have his kids help with labor on the farm? Would it be wrong for a politician to bring his family to a banquet to build his public image? What about directors that use their own children in their movies (a la Boyhood)? Etc.

There's nothing inherently wrong with having your help with your work, hell, it's probably a good thing in that it usually directly benefits the family.

In Woody's case, he has many haters that look for reason to hate, so even though everyone partaking in Woody's family movie night could figure out that he's taking advantage of the fact that people might be entertained by watching a movie with his family (and not just him), Hope directly addressing that point gives people that wish to hate a leg to stand on.

My point: Is Woody using his family to make bank wrong? No, viewers get what they want (a social movie watching experience) and Woody and his family get what they want (entertainment and money). Does the hate have a basis in truth? Yes, of course the Woodworth family was exploiting their familial status for a little extra money. Does the hate have any merit? No. There's no reason to hate what Woody did, it wasn't malicious, manipulative, or morally wrong in any way.