To directly answer your question, azithromycin is considered safe for rabbits, but most any drug in the blood will, to some degree, pass through breast milk.
I generally avoid antibiotic use unless I know what the pathogen is. Antibiotics will wreak havoc on the doe's gut flora, which is likely to make all her problems worse, and double antibiotics can result in double the trouble. When the antibiotics pass through the breast milk, the kits will get a double shot of antibiotics as well, and in an unknown dosage. Wiping out most of the bacteria in their developing guts - while possibly leaving antibiotic resistant strains! - is a pretty rough start for those bunnies. If the doe has a bacterial infection like
Pastuerella, the kits almost certainly already have it too (in fact some estimates suggest that 30-60% of
all rabbits carry the bacteria, though most are asymptomatic).
So unless you know for sure what the problem is, I'd be inclined to pass on the additional course of azithromycin. Has your vet has done a culture? If not, you don't necessarily know that a snotty nose is snuffles, aka pasteurellosis. As far as I have observed and read, rabbits do not catch viral colds like humans, but some do have allergies, and all of them can catch other cold-like illnesses, which tend to be bacterial in origin rather than viral. So "snuffles" can be caused by allergens/irritants, or by various bacteria in addition to
Pastuerella, commonly including
Staphylococcus,
Bordetella, or
Morexella. All of these have developed strains that are resistant to either azithromycin or enrofloxacin or both.
Think back to when the symptoms started. If it appeared coincidentally with a change in food, hay, or lodging (allergens, dust and other irritants can trigger rhinitis), it may be allergy-related. But if it is a condition that has come on as a result of the physical stresses of kindling and nursing babies, it's more likely a bacterial infection.
It sounds like you've already found out that whatever it is, if it is actually a bacterial infection, is resistant to enrofloxacin. Azithromycin may wipe it out, or it may not, in which case the last thing you want to do is wipe out non-resistant strains and allow a big culture of double-resistant bacteria to proliferate.
If you can assure yourself that it is not allergies or environmental irritants, you have a couple of options. Unless she is a pet that you will never breed again, I have to agree with
@ladysown that the best course of action is to isolate the group, euthanize the doe when the kits reach 4 weeks, and watch the kits for signs of infection. If she is a pet, I would keep the doe completely separate from other rabbits, pretty much forever, and probably the bunnies as well. It might seem heartless but it's actually more merciful than raising a bunch of immune-compromised rabbits that will not only suffer themselves when they encounter stresses, but which may very likely infect other rabbits, and cause heartbreak for owners who have to watch them suffer.