The Smiths had three children: Ann, Bill, and Charles. The Smiths' daughter, Ann, was a college student. The Smiths' son Bill was a soldier, and their son Charles was a director.
OR
The Smiths had three children: Ann, Bill, and Charles. The Smiths' daughter, Ann, was a college student. The Smiths' son, Bill, was a soldier, and their son, Charles, was a director.
This is my brother, Mark.
This is my brother Mark.
Both are correct. The issue here is that Mark might not be the name of the brother but the person you are addressing. You don't really have the same issue in your example. Both are fine.
I don't think I was clear enough about the problem. I think the issue arises if you remove the first sentence, so you don't know how many kids and what genders they are.
The Smiths' daughter, Ann, was a college student. ----> this implies to me the Smiths only have 1 daughter and her name is Ann.
The Smiths' son Bill was a soldier. -----> this implies to me the Smiths have more than 1 son.
Yes, a good point. This is not really a grammar question as it happens. The commas don't really help you determine whether they have one or more daughters. I think context not grammar is needed to fix this one fully. That said, I do think the without-commas version seems more "one daughter"-ish, but this is not something commas can fix for you.
