Does the wife say the supplication (O Allah, keep Satan away from us and keep Satan away from what You have provided us with) when her husband has intercourse with her, or is there another specific supplication for her?

There is no difference between men and women in seeking refuge with Allah Almighty from evils. It is recommended for the wife to recite the mentioned supplication at its appropriate time. There is no reported specificity of the naming for men; it is more apparent that women also recite it. There is no specific supplication for this situation other than the one indicated, and a Muslim is permitted to supplicate with whatever he wishes at any time, as long as it is not a sin, severing ties of kinship, or transgression in supplication.