Personality and character are not the same thing. Everyone knows that, yet the two things often get confused. Personality is something we are born with. Character is developed through the choices we make. When a teenager decides he does not want to be like his parent, it should be, and usually is, the parent's character that he wants to avoid. If he is like him in personality, he cannot help it. He can, however, be different in character.
It is exceedingly common to watch young people who strongly avow that they will not be like their parents make the same choices their parents did and become very much like them in character. This is partly because they are already like their parents in personality, and the personality influences the choices a person makes. It is our interests, desires, likes, and dislikes (in other words, our personality) that makes certain choices easier or harder.
Our choices are also influenced by the example our parents model before us. Nonetheless, we can stand back and say, Yes, I like the same things my mother likes. I laugh at the same kinds of things she laughs at, and I laugh the same way. There is nothing wrong with that -- but I am going to choose to do some things differently than she. I am not going to laugh at a filthy joke even if it strikes me funny, and I am not going to repeat it even if I want to.
If we don't understand the difference between personality and character, we might think that because we have a bent a certain direction, we have no choice in the matter, but this is the opposite of the truth. Making choices against your natural inclination is at the very root of good character. The more we exercise the opportunity to make right choices in the face of personality preferences, the stronger we become. This doesn't change our personality. We were born with that, and God gave it to us. It is guarded by our choices, but it isn't changed. There is no sin and no shame if it similar to one or the other of our parents -- even if they are wicked.
You may not want to look like your mother, but if you do, you can't help it. You may think like her and have a lot of interests in common with her, but you only act like her if you choose to. I personally am blessed with a mother I am happy to look like, and in many things I act like her also. I thank God for a mother who has made it easier for me to make right choices in many areas where another person may need a higher degree of character to overcome both inclination and example. Nonetheless, I will give account before God for each choice I have made in life, whether to be more like her or less. My personality, however, and my looks, will not come into judgement.