I'll tell you how I've done it... and what I have read about that you can put your own two cents worth on...
James harriot, the famous vet, who I'm sure embellished a lot of his stories, said he covered it with sugar for a while, which reduced the swelling... I have never tried it as it has been a *long* time since I've needed to do a full blown uterine prolapse. I think I would try it.
It has also been a while but I believe it helps to give an anastetic (spelling?) injection to immobilize her hind end... I believe it was lidocaine, 5cc in the 3rd joint of the tail.. I can't remember without looking it up... It's going to paralyse her hind legs too, so she'll be on the ground.
After you get it all washed up it helps to have a couple extra hands... one set squeezing around the vulva, and the other pushing inward... it is not something done with fists and brute force!
once you get things back where they're supposed to be, the stich I was shown was done with fairly heavy cotton string, and it might have been shoelace! I was shown to go from the inside of the vulva out, as if pinching it with your thumb and forefinger, and tying it in to a loose loop there, do this 4-5 times on each side, then use a bale twine to lace her up like you would a shoe... The reason for this is if you need to get in there again, you don't need to undo the main stiching.
Iodine, then LA200... After a couple weeks things ought to have settled and you can cut everything off..