how soft is it? does it still look like poo or is it sticking together, to her, to shelves etc? is it liquid? i am alarmed that none of the three vets wanted to investigate this further or have given you any advice. just because there's no foreign organism living in there doesn't mean it's ok.
i would advise against antibiotics given they have found nothing antibiotics would treat AND she is nursing - antibiotics get into milk. antibiotics mess up gi flora - if there something already wrong, it may make it worse. there's no such thing as a soft antibiotic for a chinchilla.
if she's not losing any weight, is nursing and behaves as normal, i would hold off any shots or harsh medication. stress can affect gi tract significantly (my mae goes into stasis if i'm gone for a day or more), it is possible having three babies is doing this to her.
i'd try probiotics. you can get them from your vet (they are aimed at rabbits) or there is a fab product called chinchilla lifeline (this is available in america, i had it urgently shipped and dawnna was really helpful and quick). there's also a product called fibreplex for rabbits, this is a paste in a dosing syringe, you can get it from your vet, the dose should be absolutely minimal - 0.5ml and then see what happens. i only used this when mae had outright liquid poo. it works extremely well but you have to be very careful, the last thing you want is to make her constipated.