From seeing everything on the internet about Law school admissions and even within in the applications themselves (C&F), transparency is prudent. It can be seen as an ethical test on your part and if you lie, you failed and most likely squash your chance of being accepted. And if your dad is an adjunct prof, they're going to piece it together that you're his child. There is a demographic section to the applications. Being forthcoming and truthful are always the way to go...especially in the legal field.

Also, this won't hurt you. It looks like most law schools want to know the reason why you've chosen their school to apply to. What better reason than a deep personal connection. Good luck!!