I wouldn't necessarily say that direct Coombs misses unbound antibodies because that implies that it is looking for unbound antibodies. Direct Coombs is used to test for only bound antibodies. The antibodies used in direct are "generic" and will bind to any human antibody. Thus direct Coombs will return positive for any condition that causes antibodies to bind to RBCs. In the case of hemolytic disease of the newborn, it would be used to test fetal blood to confirm the diagnosis.
Indirect Coombs won't find bound anti-Rh antibodies because it is only looking for unbound antibodies. The serum that is tested does not contain RBCs. For the OP's scenario, indirect Coombs would use Rh+ "donor" RBCs and will only return positive if there are anti-Rh antibodies in the maternal serum. Indirect Coombs is used to prevent hemolytic disease of the newborn.
I think the OP was asking about specificity and in this case, indirect would be more specific. Direct Coombs is actually more sensitive because if all of the antibodies are bound to RBCs, then there won't be any unbound in serum and it will return negative.