The words that do not need to be capitalized are “Family” and “Cousin.”
In terms of proper English, family titles always should be capitalized when directly addressing them. The word “Aunt” as in “Aunt Sarah” would be capitalized because the writer is addressing Sarah as the aunt. The principle doesn’t apply to the words “family” and “cousin” because they aren’t being addressed directly (in the same manner as being used). Drew is being announced as the baby cousin, but with the separation of the words with a comma, we cannot say “Cousin Drew.”
Final answer: The words “Family” and “Cousin” are not to be capitalized in the following sentence.