A simple "I don't wake sleeping toddlers. If she happens to wake on her own around that 1hr mark I will get her up but I cannot wake her up as sleep is a need, and is crucial to brain development and health".

Make it about why the CHILD needs sleep, not why you need her to sleep. Don't mention the other children, if this mom shows signs of her child being the only one that matters stick to reasons for the child.

13months is WAY too young to be depriving of sleep in false hopes of better night sleeps.