My dear brother Subhomoy,
I am really sad to hear your story.I can understand your pain very well,since I have also been in a similar situation of getting deserted by my spouse.I have also spent those years in pain.
I am sorry to know about your mother's ill health,and about your dear father's demise too.
Please do not lose hope.There's a solution to every problem.
Now you need to find the righjt solution.Don't keep begging your wife.Just collect proofs that she left you,while you are insisting on her return.For example collect copies of your e-mails,your registered posts etc sent to her.If it's proven that she's the deserter,you won't have to pay her monthly,as far as my knowledge of the law is concerned.
Although this is your personallife,a solution crossed mymind just now.But it depends on you,if you want to follow it.
Is it possible for you to shift near her school,if it's not that far.This way your old mum,and child will be looked after by both of you,and this marital mess will end.But before shifting,you have to also analyse its pros and cons v.well,or else you suffer later.
If that's not possible,you follow your hear and think of your self respect.