Superlative and definite article "the"

Neither sentence is a natural English sentence. Teachers like to make multiple choice questions and create artificial sentences, and there is a danger that they are not actually things any one would ever say, but really it is a matter of the context. Any technically grammatical sentence, as both of these are, could be valid in an appropriate context.

If the teacher is not a native speaker of English, the made up sentences are more likely to be spurious, and often are not grammatical even in the so-called "correct" case.

The difference between these two sentences is very slight and subtle, and if I was forced to choose I would choose the version without "the", but if I dropped the "in the family", I would reverse this preference because there is no longer a comparison set, so a unique person in the universe is being identified!! There is nobody in the universe that gets up later - and even for our planet, with our various timezones, this doesn't really make any sense.

The article is not obligatory. There are two constructions here:

• latest is adverbial and relates to the manner in (or in this case, time at) which she wakes, or;
• the latest is part of a noun phrase where a node sister to the adjective latest is omitted - for example, She gets up the latest [time] in her family.

They're both grammatical because they're different constructions, and if you parse the syntax, they have different structures.