Not sure if they have coaching for 3 year olds...but do check Tilak Tank (Deccan Gymkhana Club) on Prabhat Road - Pune's largest (quite possibly India's largest) swimming pool. They have extensive coaching programs across all ages.

Tilak Tank has a near 100 year old history and has produced many national level champions.

Checkout: http://www.deccangymkhana.co.in/swimming.aspx

Baner / Aundh - Try Mobius. They have coaching. Last year @Rs 1000 p.m.

Baner / Balewadi - Try the Balewadi sports complex. They do have coaching, but am not sure from what age.

There is one very good swimming pool in Wanowarie, Sivarkar swimming pool near sivarkar garden. I learned swimming there. I saw a lot of kids 3-5 years getting trained. Teachers are good. Fee is very economical. Great safety measures. I fully recommend it.

hi iam vaishali my son is 2 years & 11 months and he Swimmimg well. he daily goes to shree water tank. vimannagar. i am very satisfy about his coatch.

There are many swimming classes but not sure which provides training for 3 year old. Here is list of Swimming classes. Hope it might help you.