There are one or two comments I would make, which you may find pedantic, but, that notwithstanding, they are true. There is, and never has been, a blood group system named Rhesus. Rhesus was an ancient king of Thrace. The correct name for the blood group system is Rh. So, it is the Rh Blood Group System, the two genes involved are RHD and RHCE, the carrier proteins are RhD and RHCcEe, but the antigen of which you are talking is just plain D, and not Rh D.
There is a very good reason why the instructions that come with the anti-D state that the tests should be read macroscopically. Thorpe et al, in two papers, reported that monoclonal anti-D molecules possess a V4-34 moiety, that is also present in anti-I and anti-i. As a result, if papain-treated D- red cells are tested with such antisera, or untreated D- red cells are tested with such antisera that have not been brought to room temperature, they may agglutinate. This could result in D- red cells being mistyped as D+ - a particular danger in females of child-bearing potential, and babies (Thorpe SJ, Boult CE, Stevenson FK, Scott ML, Sutherland J, Spellerberg MB, Natvig JB, Thompson KM. Cold agglutinin activity is common among human monoclonal IgM Rh system antibodies using the V4-34 heavy chain variable gene segment. Transfusion 1997; 37: 1111-1116, and Thorpe SJ, Ball C, Fox B, Thompson KM, Thorpe R, Bristow A. Anti-D and anti-i activities are inseparable in V4-34-encoded monoclonal anti-D: the same framework 1 residues are required for both activities. Transfusion 2008; 48: 930-940).
In addition, if you do not follow the manufacturer's instruction, and something goes wrong, under UK (and EU) Law, you could well be liable, as described by Bob Doughty some 30 years ago now (Doughty RW. Product liability in the medical laboratory. Medical Laboratory Sciences 1989; 46: 68-71.
In the case that you describe, do you know the Weak D type of the baby (it may well be Weak D Type 2, which can be particularly weak) and, at any time, did you test the mother's red cells to see if she was also a Weak D of the same type? If she was, then it is highly likely that anti-D immunoglobulin would not have been required anyway, although I am aware that this is not part of the BSH Guideline (White J, Qureshi H, Massey E, Needs M, Byrne G, Daniels G, Allard S and British Committee for Standards in Haematology. Guidelines for blood grouping and red cell antibody testing in pregnancy. Transfusion Medicine 2016; 26: 246-263. doi: 10.1111/tme.12299).
My honest advice is that you do not read the tests under a microscope. If you have ANY doubt, give the mother anti-D immunoglobulin anyway - it is not that expensive, and has a good safety record in terms of TTI.