I am not admitted in Michigan. Threaten you with what? Actual proper service of divorce papers? I wouldn't sign a thing. It is when they are served that matters here.
And for the portion regarding your son, if you are contesting it it is doubtful that the court would give her sole custody except in extreme circumstances. The court uses "the best interests of the child" as criteria for determining custody issues.
Sounds like your wife is just angry. If you think that she is serious get yourself a lawyer.