Are you sure she is in full labour? she could have a vaginal prolapse which will keep popping out until she lambs, in which case i would pop a spoon or harness on her until she fully lambs. If she is in labour and lambs are up in the canal ready to come out, if she has four smallish lambs i would personally lamb her the old fashioned way before doing a c- section. if she then prolapses fully and you can get the womb back in ( try shrinking it back with sugar) then apply a harness to keep it in.
I would think this would be better than opening her up, but this is my personal view.
It will also depend on your ewe and how strong she is, if she is showing real signs of distress then go with your vet he has the knowledge to deal with these things but i am suprised he is going for a full c- section before trying to lamb her naturally. Most prolapses are alleviated by the lambing process.
She will need meds no matter how you proceed anyway, antibiotics and painkillers and i have known c-section ewes bring up lambs but it will depend on how strong she is, i would have thought 4 would be too many for her to cope with, maybe just one or two and foster the others.
Good luck anyway