A mixture model will be fine.
But on a general level I am trying to figure out the equations for the EM algorithm:
However, a Maple demonstration would be great.
My other questions (tetrachoric and polychoric correlations) could probably be solved with the 'fsolve' command and a bivariate normal distribution (as suggested by a collegue). Comparing observed proportions in a contingency table and expected proportions in a bivariate distribution with a fixed correlation coefficient, but at least for polychoric correlations it has to be solved iteratively.
In R the code would be available, but to translate R into Maple may not be an easy job.