Is it permissible, in Sharia, to go to a mother who has left Islam and works in a bar?

If the intention of the question is to visit the mother, there is no harm in that. Her right to dutifulness and maintaining ties remains even after her apostasy, while being keen to advise her and remind her of the gravity of apostasy. However, if the intention is to reside with her, that is not appropriate, due to the danger it poses to your faith and character. It is more fitting to remain with the father, be patient with him, and treat him well, for that may be a cause for rectifying the situation between you. And you must be patient with the harm caused by the stepmother.