Is it permissible to report an ex-husband to the police for not fulfilling his marital obligations, especially given that he has committed legal violations?

If you know that reporting to the police will not restore your right, then it is better to abandon it; for Allah will enrich you and compensate you with something better. Allah Almighty says: (But if they separate [by divorce], Allah will enrich each of them from His abundance. And Allah is ever Encompassing and Wise). He will be recompensed in this world or the Hereafter, and your reward for your patience and your attempt to guide him is preserved. Going to court would be a victory for the self and would diminish your reward, so seek your reward from Allah and ask Him for a better compensation, for the relief from Allah is near, and whoever gives up something for the sake of Allah, Allah will compensate him with something better.