Quick update- funny, the vet called RIGHT after I posted this!
Petey has a non-communicable viral infection! This is one that's easily treatable with a variety of antibiotics! Currently, he's taking them via water, which is being changed out several times a day. However, they would like him to be on liquid drops, which I would have to administer to him. If I'm able to do this, and he's a good budgie and takes them, he will be able to go back into the cage with Olivia and the baby! YAY! If not, it's OK to continue using the powder antibiotic we're on, but he'll have to stay in the nursery cage so Olivia doesn't get the meds through the water.
Anyhow, this is good news!