Can employer force me to serve full notice period

Hi, As my current company is insisting me for relocation to another city which I am unable to do due to my family issues, hence I have resigned from the company after getting a new job in my current city. As per my employment offer, the notice period is 60 days & the notice period clause is mentioned as "THE MANAGMENT MAY IN ITS SOLE DISCRETION TERMINATE YOUR APPOINTMENT BY GIVING A MONTH'S NOTICE OR PAYMENT OF SALARY IN LIEU THEREOF. LIKEWISE, YOU WILL BE FREE TO RESIGN FROM THE SERVICES OF THE COMPANY BY GIVING A MONTH'S NOTICE OR PAYMENT IN LIEU THEREOF. THE MAXIMUM AND MINIMUM PERIOD OF NOTICE FOR TERMINATION, HOWEVER, WILL BE TWO MONTHS". The new organization is willing to wait for 45 days but not more than that. I have asked my management for an early release with 30 days notice period & now I am extending the notice period to 45 days but still they are insisting that I should serve full notice period. I am ready to pay or adjust my leaves against the 15 days that I will not serve but still the HR is threatening that the employer is fully covered legally & may take legal action against employee if I will not serve the full notice period. I have also offered my current company that I am ready to work during the weekend holidays to cover the lost days after the early release before 15 days of notice period without any extra compensation as I want to leave the company with a good note but still they are very rigid & not allowing to give the release before 60 days. Can the company force me to serve full notice period? Please advise. Can I leave from the services before 15 days of full notice period and join the new employer? Thank you in advance for your kind assistance in this regard. Thank you