To apply for dependant VISA in India, All you need is 6month's Bank statement, 6 months Pay Slip, Letter from you employer and Mortgage statement or Letter from the home owner.
You also need original full Birth Certificate of your son or daughter and copy of your passport showing your VISA Status.

I have got dependant VISA for my son in India only. He was born here and traveled to India in his indian passport obtained from birmingham.
There were no problems in travelling to india. Only while coming back you need UK VISA. It is much cheaper to apply for VISA in UK embassy in India.