Learn English – plural forms – family names

There is no rule determining whether or not a noun's plural form is the same as its singular form. As the comments point out, many of these words are words for animals. Another trend I have noticed is that loanwords from Japanese often don't change in the plural (two kanji, three Pokemon, ten anime), though sometimes they do (six ninjas, eighty futons).

Your daughter's textbook is not quite accurate.

You capitalize such nouns when they act as names, as the ordinary form of address. "Mommy" is used that way in your second example.

But in your first example, sister is not a name, as its use with a determiner makes clear: it is a common noun denoting a relationship.

If the determiner is omitted, however, the noun is treated as a name, and it is proper to capitalize:

Ask Sister. She's fond of playing on it.

That sort of use of sister is rare, although not unknown; as Damien H says, Sister, capitalized, is usually the title (of reference and address) for a Catholic nun.