Not a prolapse. Just the tail of the placenta, which, if it still hanging out of her after this length of time, indicates a retained placenta and watch to make sure she doesn't get sick.
The discharge looks like some retained placenta. The other area appears to be a swollen vulva from caving. Uterine prolapses tend to be farther out and have red "buttons" from where the placenta was attached. Also have a more "wet" appearance if they are fresh.