Um, more to the point, not how fast it gets from mother’s milk to baby, but how fast, how much, and WHETHER it passes from mother’s bloodstream to mother’s milk. Ingestion is ingestion after that.
The process for substances passing into human milk is pretty complex - pH, whether it is a fatty substance, and a variety of other factors affect what passes and what doesn’t. I’m sure the same issues exist for cattle. It has been a while since I read the general data on what actually passes through, but if I recall right, most hormones do NOT pass through, but some do, and some do in limited quantity (such that the amount is stable no matter how much mom is making). Antibiotics generally DO pass through. Prescription drugs of various sorts have various levels of excretion into milk. Most don’treach serum level (bloodstream level), but a few seem to concentrate. Same for nutrients - if you overdose on your vitamins, in most cases the impact on the vitamin level in the milk is NONE. But a few DO end up concentrated.
One of the things that people forget is the whole serum level thing. If you give someone a dose of antibiotics, then take a serum sample (blood-test, say), the concentration of the substance is WAY lower than a prescription dose, and they may also already be metabolized into a differnt form - which then may or may not break down further in the digestive system if consumed in the form of milk. Given that milk-levels may be well under serum level, and that you are then using a very limited amount as input (in the milk, in this case), most impacts will probably be subclinical, if evident at all. Most drugs require a threshold to SEE any impact (though there may be some impact technically, it isn’t enough to cause a change in development, cellular process, or whatever). You could be eating a measurable amount of all sorts of things every day, and never see a direct impact - that’s why we have such redundant development processes (IMHO), to keep the minor impacts from becoming significant.
You still have to figure out what level actually ends up in the milk in the first place. And you can’t generalize AT ALL - you have to test it, and see if it actually does come through. Antibiotics DO come through. But the issue there is creating resistant strains of bacteria by exposing them to low levels of the antibiotic on a regular basis.
overall, it is amazing how little impact you can have on milk content. You can be damn near starving to death and your milk quality will be damn near as good as a woman who is on a well-balanced diet (with only a few nutrients out of balance and the rest identical between sources)- it doesn’t make sense, but it has been tested again and again. Anyway, this is by way of saying, ‘Be careful not to assume that milk production is a simple excretory process - it isn’t GIGO, it is a very selective production method.’
For the OP question, yes, most kids go through cycles of food ‘kicks,’ and they do self-regulate to a fair degree. But they are also a bundle of obsessive/compulsive bahaviors, and can easily develop habits that counteract the natural balancing system. (and if it bugs mom or other grownups, all the better!) Milk I think is slightly better than juice, but I agree that overdosing on any liquid is a matter for concern - not panic, but concern. I think the general rule I was given was to average the consumption over 2-3 months, and see where you ended up. My son will eat 60% PB&J for 6 weeks, but then he’ll be off onto something else. Like broccoli. I keep giving him a vitamin, and wait hopefully for the day when he’ll eat something different two days in a row. 