From what I have read at the LLLI website on "Breastfeeding and the Law",
there is a good chance that the father will be granted overnight visitations
because the baby already has lengthy day time separations from Mom. The father
may find out for himself that the baby needs her Mommy at night and step away
from the issue for a while (one can hope!)  The other scenario could be that
Father and baby find their "own way" to get through the night without Mommy
(and perhaps Mom fears this, in a way).   I have helped quite a few Moms who
work overnight shifts where Daddy is the caregiver, and baby simply spends
more time sleeping when Mom isn't there, then plays catch up all day the next
day/s to make up not only for lost time at the breast and milk, but also to
catch up with Mom.
  That being said, the Mom in this situation would do well to stress the
attachment of mother and baby and take the focus away from breastfeeding.  A
ten and a half month old, no matter how they are fed, may be very unhappy at
night away from his mother and sleeping in a strange place.  If the father is
a sensitive and reasonable one, he will put his baby's needs before his own.
I hope that they can settle this out of court, too, without a lot of arguing
and fussing, for the sake of everyone involved.

Lisa Jones, LLLL in Wellington FL