hey, miti! :--)
glad the pup was all right - yes, i agree that would be frightening!
any bitch with newborns is twitchy...

but a 15-WO pup, even a F pup, should still be under the usual puppy-license, and should need to do something pretty bad to rank a real set-down + potential injury from a varmint-type assault

(bite + shake is an intent to maul or kill, not merely a warning; it is normally reserved only for prey, or for an adult dog or older pup past 5-MO who is a genuine threat of some sort - biting, fighting, threatening, entering the puppy room AFTER being told to go off, etc).
so i would say this was a very serious wake-up or heads-up warning -
Airedales are unfortunately terrierists, and the BIGGEST terrierists of them all, too.

they do have the same unfortunate tendency to dog-aggro + reactivity found in most terrier-types, from Westies to Yorkies to JRTs to Bedlingtons.
when her pups are at least 6-WO, i would ask the rescue-folks to do a dog to dog behavioral eval... just take her into the presence of a few NON-threatening, dog-social dogs of both (desexed) sexes, and at a distance, read her reactions in her emotional signals:
is she up on toes?
is her tail up, stiff, or flagging slowly + high, like a metronome? (Look out!!)
is she leaning toward them, or attempting to loom-over them?
does she freeze or stare?
is her MOUTH closed, with tight cheeks or puckered whisker-pads?
(indicates tension + suspicion)
all of those are bad signs -

if she displays any 3 of them, i would be concerned.
if she shows ALL of them, even at a distance of over-20-feet, i would consider her to be in need of a good pos-R B-Mod re other dogs, to alter her emotional response!
good luck, hope it was just raging hormones + a one-off,
or maybe the pup did jump on her in an attempt to play, and hurt her stitches...
fingers crossed,
--- terry