As per the above mentioned scenario ,the husband's attitude is condemned as per Sharia Laws. He has no right to leave his wife in this situation. Without going into details, it is obligatory on husband to fulfill physical desires of his wife. Yes, he would be punished if he doesn't fulfill his obligatory duties.
Such a behavior of a husband can't justify the wrong means adapted by a wife to fulfill her sexual desire. She has to seek some lawful means. She needs to try all the means to make her husband understand her feelings and if nothing works, the last option is Mubaraat divorce.
However, the behaviour of such a husband is strongly condemned in Islam.