Correcting Young Toddlers/Babies

My wife and I have a 15 month old daughter who has recently been yelling and crying to communicate her frustrations, particularly in response to a no answer. When we try to correct her for not accepting a no answer she will often try to squirm out of our arms, ask to eat over and over, or pull her mom's hair. At that point, should we finish with the correction we are giving or correct the recent behavior of pulling hair, etc.? What would you do?