M.L.
This sounds weird, but do you have any Nature's Miracle around? That's the stuff that removes pet smells and stains. However, I know from experience it deals with more than pet problems.
If you can borrow some (or buy a small bottle), give it a try. The egg and its, um, accompanying fragrance may have gone through the fabric into the stuffing. You'll need to soak the spot in NM, even the cushioning; it has its own odor when it's wet, but when it's completely dry, both the smells should be gone. Worth a try, maybe.
Also, I just went online and found this site which may help you:
http://www.thegeekcity.com/how_to_get_rid_of_rotten_egg_s...
My goodness! You're very brave to have a white couch in the same house with children! :~)