Multiple impute multilevel data and postestimation tests

Question

I want to do the following three things but am not sure how/whether they can be done:

1. multiple impute multilevel data. I would be ok with just accounting for clusters, but I need to somehow account for data structured such that children are nested in parent-child dyads, nested in families.
2. use seemingly unrelated estimation on imputed data to estimate analyses on mother-child and father-child dyads separately
3. compare coefficients across mother-child and father-child dyads using a Wald test (or some other appropriate test).

I have already done the unimputed analysis in stata, so specific tips for stata are much appreciated, but any program is fine.

EDIT: I SOLVED THIS PROBLEM (or got close enough) AND AM POSTING THE ANSWER IN CASE ANYONE ELSE HAS THE SAME PROBLEM. If you see something wrong with my answers below, please let me know!

1. Impute multilevel data: I first made the data "wide" so that each row is a family, then I imputed the data. This at least accounts for clustering at the family level, though ignores clustering at the dyad level.

2. Seemingly unrelated estimation, step 1 (estimate two equations with common variance-covariance matrix): using the "mi" command for multiple imputation in Stata doesn't save the estimated coefficients, so the usual "suest" command doesn't work. I wrote a program that would save the estimates and feed them into the suest command.

3. Seemingly unrelated estimation, step 2 (Wald test): I couldn't figure out how to do a Wald test with a chi-squared distribution, so I did a t-test in the form of t = [Model1]var1 - [Model2]var1 using the estimates saved in step 2.