First of all, the purring is a GREAT sign -- that means she's putting up a fight! :smile:
Cats are notorious for difficult to regulate BG's, so that's not at all surprising to me, especially when there's a UTI in the mix. I'm sure they've got her on antibiotics to knock that out. Liver values, etc. are typically a train wreck with DKA, however they can snap back to normal very quickly once they get the BG and infection under control. Ultrasound is the logical next step. She may have dumped some fat into her liver, as my cat did. That can take a bit to clear as well and they really can turn the corner amazingly fast.
Glad to know she has proper, competent care. Sometimes regular vets attempt to handle these cases when they just don't have the necessary critical care experience.