Dear ck,
Wow! Your husband did an incredibly thoughtless and unwise thing. However, that being said, I am reminded of Jesus' story of the Good Samaritan (Luke 10:28-37) You will recall that an expert in the law asked him "And who is my neighbor?", and He went on to recount the story we all know so well. At the end, Jesus asked the expert, “Which of these three do you think was a neighbor to the man who fell into the hands of robbers?” The expert, of course, answered “The one who had mercy on him.” And jesus replied, “Go and do likewise." (emphasis added)
There are many things left unsaid in your post. What is your relationship with your husband's ex wife? What is his? Do you have any reason to believe that your husband would be unfaithful? Does your stepson want to see his mother? Can his ex wife afford to stay somewhere else while she visits? Is there anywhere to stay? All these factors, I believe, enter into the equation.
Being a Christian means being a Christian even when it is not comfortable to do so. If there is no reason to believe that anything bad will come out of this visit (other than you being incredibly uncomfortable), I would suggest that you consider taking the high road and letting it happen. You can let your husband know that you are very disappointed that he didn't consult you first, and you would not want to see it happen again, but getting into a fight will not solve anything.
God be with you in your struggle.