Did the vet not know how many pups (roughly) she was having before? (by feeling her abdomen?) If it was me, I would move them to a clean dry space, as long as Millie is OK with you moving them. We had a dog many years ago that had her pups at home but we were fully prepared with whelping box etc inside. I'd be keeping my distance but not be taking my eyes off her just to make sure.

A friend of mine who had OES pups recently took her to the vet coz she was not progressing and the vet did not act quick enough (left the dog more than an hour between pups) and as a result she only ended up with 2 out of 6 puppies.

If the 2 pups she's had are feeding and everything OK they I guess they should be fine. Millies obviously taken them out of their little sacks and eaten their placentas (ewww!) Can your vet do house calls? If not, I'd take them all to the vet to be checked out in a few hours or so especially since they've come early.

Good luck and congrats Millie