For re-extension of joining date(joining period is 30 days, one extension was taken 30 days by me form the approval authority )

Dear Sir, i have selected for govt. contractual job and its notice period for joining is 30 days but i have extended to another 30 days, still i am not relive from present organisation. They are unwilling to relive me due to some project obligations and at mean time a family emergency arisen in connection with my mother’s health . Being the responsible member of the family (and the present organization), I need to take care of the situation and look after my mother’s medical condition which demands a considerable minimum amount of time of 2 months (60 days) Under these circumstances, can I extend my joining date for extra 2 months (60 days)? please guide me in his regards.