I know that it is possible to have some control over the correlation parameters with brms. I’m wondering if it is possible to use the same correlation matrix in two parts of a model, but to have different vectors of scale parameters.

Is the vector of scales meant to be passed as data, or is it meant to be estimated? If the vector of scales is meant to be passed as data, then you can just form the two (different) covariance matrices M1 and M2 and then use

If the vector of scales is supposed to be estimated, what information do you think the model is going to use to estimate the vector of scales? There will only be one sample of group-level effects from the multivariate normal random effect distribution, which isn’t enough to estimate a vector of scale parameters. You can’t usefully fit a multivariate normal distribution to a single sample, even if the correlation matrix is known.