Yes, both are correct. The plural families is needed in the first sentence, and so families' is correct. In the second, it's singular and so family's is correct. It would still be acceptable in my opinion to use the plural families' in the second sentence also, since technically we are talking about many children and thus many families. However, I would write it the way it is. It is easy and natural to think in terms of one individual family at a time. Some may quibble about it, but I say let 'em quibble.Hi - Can someone tell me if the following two sentences are correct usage of posessives?
The center is committed to meeting families' specialized communication needs regardless of their ability to pay.
The goal of the Center is to continue to serve all children in need of services regardless of their family's ability to pay.
Note that some people tend to dislike adding the possessive to plural nouns unless really necessary, and so might phrase the first one as "the specialized communication needs of families," thus eliminating the need for the possessive form. However, it is correct as it stands.