So you have 2 groups and in each group you have a dichotomous factor? And you are estimating a difference for each group? And then comparing the 2 differences? Did I get all that correct?
If so, I would construct a single model with 2 separate parameters (one for the difference in the one group, the second for the difference in the second group). Your trace will then contain samples that reflect the joint distribution of difference 1 and difference 2 and you can then directly ask about p(diff_1 > diff_2). Does that make sense/work?
If you dump in some code, we could sketch out a more concrete solution.