Oh hon, I'm so sorry you & your girls are going thru all this trouble and you could do nothing but trust the vet and they are not always the most knowledgable, experience counts for a lot. I'm glad you're here, you will get good info. Still you will run into completely contradictory suggestions, nobody would try to steer you wrong here, but with ratties some things are trial & error, and the rules change according the the problems sometimes..
So, another opinion to confuse you....
First I would absolutely treat them for mites right off the bat. There's no harm in it even if you're wrong. You can find info here how to do that. You'll run into 2 schools of thought, mine is Ivermectin, the other is I believe Advantage or Revolution? You MUST scrub & rinse all their space really well, and toss anything that is not totally scrubbable (or else freeze it for a long time - is it a month or 6 weeks?). Mites can hide in crevices and wood is full of crevices. Ask for help if you need to.
Next is to get some food into Aylie. Again you run into divergence, rats are said to be lactose-intolerant but I've never experienced it, so yours may or may not have a problem. But if one is on antibiotics it's not only highly beneficial but but also suggested to give them yogurt to counteract the stomach troubles it can cause. See? Gets confusing. And best food guide goes out the window when a kid won't eat. Ensure or Boost are your best bet. They are good 3 days in the fridge after opening but you can pour a can into an ice cube tray, freeze, and use as needed. Adds weight, they take it readily (try different flavors) and it has all the vitamins & nutrition they need. Fattening foods are avocado (yes, it's ok for rats but not other critters), mashed potatoes, mashed yam, perogies, bananas, anything she'll take.
Use warm compresses on any lumps, burst or unburst. If one opens try to gently express any stuff in it by always putting fingers under and pushing up toward the opening, you don't want to push anything down into their body (warm compresses help bring it to the surface). A couple times a day. I always used 50/50 hydrogen peroxide/water to dab the opening after.
I don't think you said what antibiotic Aylie had? Baytril/Doxy is usually the best antibiotics to start with for respiratory problems, and others like Zithromax if they are not clearing up,but other problems can be better served with other antibiotics like Chlor-Palm. Many vets prescribe for a week or 10 days and often underprescribe the dosage. This can cause them to build an immunity that can keep them from ever getting cured completely. They really should do 2-3 weeks at least. Consult this:
http://www.rmca.org/Articles/dchart.htm and share it with your vet. You can get good experienced suggestions here and hope your vet is willing to learn from what's worked from other vet's prescriptions. A lot of vets will resent you coming in with any questions or requests you learned online, but as long as you're paying the bill your kid's wellbeing overrides any threats to their insecurities about their omniscience.
I took Dona to the vet, vet was mystified, injected her with Ringer's and gave her an Rx for baytil, I told Jorats online what Dona was doing and she said PT right away, she was dead right. I took Summer to the vet when Baytril didn't work and asked for Zithro as lilspaz suggested, she refused and gave me Erythromycin, Summer died. I took Kelley to the vet, she suggested meningitis, doubt you will ever hear of a rat with meningitis here, it was PT. Other stories too... Vets aren't god but they do hold your kid's lives in their hands and sometimes you need to know what to beg for. This place has more knowledge than my vet does. And a lot more comfort & support when you need that.
Treat for mites. Absolutely give her yogurt if she's on antibiotics, give her Ensure or Boost & any fattening food she'll eat. Ask for help here & do your research to try to get the right things from your vet first visit (nobody can afford multiple visits while the vet flounders).
You've been thru the wringer. Welcome to the font of knowledge (chaotic as it can be) and loving understanding hearts & arms. I hope it can help you & your girls like it's helped me & mine so often..