Do you mean the Beta-coefficient is negative in one model and positive in the other?  Or the odds ratio?  If Z in the second model is negative, then X2 must be negative.  It also appears that in the second model, Z is a function of the inverse of X1 and multiplied by X2.   I think there really is some kind of multicollinearity, but it is not linear.  You could try to simply transform Z by itself without making it a function of X1 or X2 (without using X1 or X2 in the model), and enter the transformed Z-value into the regression, if that would make sense.