Recent studies have shown that providing personalized explanations alongside recommendations increases trust and perceived quality. Furthermore, it gives users an opportunity to refine the recommendations by critiquing parts of the explanations. On one hand, current recommender systems model the recommendation, explanation, and critiquing objectives jointly, but this creates an inherent trade-off between their respective performance. On the other hand, although recent latent linear critiquing approaches are built upon an existing recommender system, they suffer from computational inefficiency at inference due to the objective optimized at each conversation's turn. We address these deficiencies with M&Ms-VAE, a novel variational autoencoder for recommendation and explanation that is based on multimodal modeling assumptions. We train the model under a weak supervision scheme to simulate both fully and partially observed variables. Then, we leverage the generalization ability of a trained M&Ms-VAE model to embed the user preference and the critique separately. Our work's most important innovation is our critiquing module, which is built upon and trained in a self-supervised manner with a simple ranking objective. Experiments on four real-world datasets demonstrate that among state-of-the-art models, our system is the first to dominate or match the performance in terms of recommendation, explanation, and multi-step critiquing. Moreover, M&Ms-VAE processes the critiques up to 25.6x faster than the best baselines. Finally, we show that our model infers coherent joint and cross generation, even under weak supervision, thanks to our multimodal-based modeling and training scheme.