Invite your wife after your friends have said they will come.
Why invite her at all? Why not invite the friends and do not even tell her about it. If she shows up, great. If not, who cares? If she shows, she will wonder why she was not invited. If she does not show, she will probably be asked by someone where she was or be told what a great time they had without her.
God is love, love is blind, Ray Charles is blind......so there.