It looks a *lot* like a prolapsed vagina/uterus I saw on a cow once... I got to hold her tail up and out of the way while the vet did the 'reorienting'.
It's a lot easier to deal with prolapses in cows, if only because the structures are bigger - coat disinfected arm up to yea in soap flakes, and then just... guide it back to its rightful spot. Yicky I know. Obviously I wouldn't recommend even trying that with your girlie - besides the structures being tinier, they're also more fragile.
KY jelly would be the order of the day for your girl - don't use petroleum-based lubricants if she stands a chance of eating them. Barring that, some kind of oil like olive oil might be okay... and Shelagh's right, this is an emergency-surgery type of situation.