Out of the given options, option D provides the best elaboration on Michele's sentence about being a single mother to two young girls while also relating it to the reason for writing the letter - the ability to cover extra shifts.
Option D expands on Michele's statement by providing the additional detail that her mother lives with them and can watch her girls when needed. This directly relates to Michele's ability to work extra shifts if required, since childcare is available.
Options A and C provide personal details but do not directly connect it to Michele's ability to take on more responsibility at work.
Option B does not improve or elaborate on the original sentence at all.
Therefore, option D provides the most relevant and meaningful expansion on how being a single mother of two girls with her mother's support allows Michele to cover extra work shifts if needed. The extra detail is informative while directly supporting the purpose of the letter.