If you and your wife want to live like students, yes, you can do it. But probably not for very long before she gets bored and frustrated with the low budget and boring lifestyle. (Not being able to communicate with the locals and five months of winter is going to work on her nerves as it is).
An apartment, rent, fees and utilities included, is going to cost you between 2000 and 2500 PLN a month. That leaves only 1500 to 2000 PLN a month left over for food, household supplies, clothing, electronics, entertainment, travel, diapers and baby supplies, furniture, etc.
Of course, forget about it if you have to for airfare out of your own pocket. That would put you deeply in the red. Nor would you be able to afford any trips back to India for your wife or you.
Sorry, but moving to Poland with a wife and kids doesn't make much sense unless you are RICHLY compensated. It would make more sense to send the wife and kid back to India, and come to Poland on your own.