Can father divide property in name of mother and son's?

Yes, your father can give the property to his wife as she is also a Legal heir. As per law if your father dies without a Will then the property will devolve amongst all his legal heir including your mother and sister.

If the property is self acquired property and not an Ancestral Property or HUF (Hindu Undivided Property) then the father can do whatever he pleases with the property which includes giving it or a share of it to his wife.

you father in his lifetime can do whatever he wants to if the property is not ancestral,meaning if the property was owned by your grandfather,if you fahter has purchased it with his own income he can during his lifetime divide the shares as per his wish.The mode of dividing would be gift deed to each son and wife defining the percentage of share.