Hopefully, your wife made the decision to undergo her procedure with a board certified plastic surgeon, because, now more than ever, she really needs the expertise of a fully trained surgeon to handle this wound. Your obstetrician, dermatologist, and oral surgeon will never have as much background in managing this type of problem as someone who has received their training in plastic surgery.
Having said that, you will be in for a long period of scabbing, deepening of the wound, daily dressing changes, and then eventual healing. The amount and prominence of the scarring is unpredictable, but it is very likely to be quite a bit wider and more visible than had this not occurred.
In the meantime, follow the advice of your surgeon. At some later point, together the three of you will be able to consider whether revising the scar is possible and/or helpful.
Best of luck.