The best reference I could find on this was Schwegler et al. (2013), which gave detailed descriptions of both the processes of transfer of alcohol to the bloodstream and breast milk and the effects thereafter in the mother and the infant.
Here is a somewhat condensed timeline of what happens.
Intake. The mother consumes an alcoholic beverage, which travels along the digestive tract from the mouth through the esophagus and into the stomach and intestines.
Resorption. The alcohol (really ethanol, for all intents and purposes) is resorbed in minute quantities in cells in the esophagus, and in moderate amounts in the stomach. Most of the resorption takes place in the intestines and beyond, specifically the smaller intestines, thanks to the "first pass effect". The ethanol is now transferred to the bloodstream.
Breakdown of alcohol. The ethanol is transformed into metabolite acetaldehyde via alcohol dehydrogenase (ADH). ADH is more common in the liver and intestines than in the stomach, which in part accounts for the higher resorption rates in the lower part of the digestive tract. Next, the acetaldehyde undergoes oxidation by aldehyde dehydrogenase (ALDH) or monooxygenase CYP2E1. The result is acetate, which is then turned into water or carbon dioxide, as normal.
Transfer from the bloodstream to breast milk. This step happens concurrently with (3). Some of the ethanol circulating in the bloodstream is transferred to breast milk along with other substances. This transfer often contains ethanol that has been resorbed from the stomach, where less ethanol is resorbed and filtered away. Additionally, acetaldehyde is generally not present in breast milk (Kesäniemi (1974) is cited on page 16). The reason for this is unknown, but it points to the absence of ADH.
The upshot of all this is that there may be little to no breakdown of alcohol in breast milk. Breakdown via ADH and ALDH would happen between resorption and transferal/lactation.
Levels of alcohol in the blood and in breast milk are generally the same, thanks to diffusion between the various glands in the breasts and the bloodstream (note that there are, of course, specialized veins and arteries for the mammary glands). Diffusion out and in means that there is not a significant net gain or loss of alcohol from the breast milk.
One reason for different concentrations in different groups of women depends on how proteins responsible for the filtering and breakdown are released. The authors say (page 16)
To explain the observed differences during lactation, Pepino et al. (2007)
hypothesised that increased levels of regulatory proteins are released during the breastfeeding phase and that these proteins delay the passage of the alcohol from the stomach to the small intestine and liver, thereby increasing the first pass effect. The findings were confirmed in a further study by Pepino & Mennella (2008) among mothers who pumped off their milk.
It's worth noting that only a small amount of the total amount of alcohol makes its way unfiltered into breast milk. As Menella (date unknown) writes (emphasis mine),
In general, less than 2 percent of the alcohol dose consumed by the mother reaches her milk and blood. Alcohol is not stored in breast milk, however, but its level parallels that found in the maternal blood. That means that as long as the mother has substantial blood alcohol levels, the milk also will contain alcohol.
This is the key principle. Basically, there is little to no breakdown of alcohol in the mammary glands, due in part to the lack of ADH. While some enters through the bloodstream, it can diffuse out and be broken up in the normal fashion.
