I think what you are looking for are sometimes called vector autoregressive (VAR) models, and there is currently no such autocorrelation structure in brms; as you said ar() just gives two independent ar terms. (Further it does not give each “subject” their own ar term, which might be something you’d want?) It also looks like there are latent variables in your model which currently have very limited support in brms, but this might change in brms 3.0.
One thing you can try is to manually create the lagged variables and use them as predictors (and/or outcomes). There’s been some related discussions here, and another recent related question here.