The Catholic Church teachings and the death penalty

Last night I was able to spend the evening playing penny poker with my extended family members ( as a side note, I ended up winning a dollar in pennies... so if we were playing with dollars I would have made a nice amount... my Aunt wanted to take me to Vegas with her to win her some money...) and we somehow got on the topic of the death penalty. I have mixed feelings about this topic as it is, but having to listen to my family debate over this issue brought some interesting things to come up. I know that my dad happens to be a believer in the death penalty, and although he is, I am still not at all happy with the whole idea of it... What really got me was how one of my cousins who is very against the death penalty happens to also be pro-choice, which I cannot really understand. She seems so worried about convicting innocent people to the death penalty, but she is okay with killing an innocent baby who also did nothing wrong... I am not quite sure how she can be okay with killing that baby, but not okay with killing someone who was innocent, but found guilty. It seems like those two things kind of go hand in hand to me, but what do I know. So as my family was debating this topic, I decided to not make much head way, mainly because in my family when they get into one of these heated debates you kind of have to yell to get yourself heard, plus I had started to get a head ache from hearing way too many people talking all at once. Instead I would look at my cousin who was standing next to me and feeling in the same boat as I was and occasionally add a comment to him here or there. Today I started thinking more about this whole death penalty issue and decided I'd look up what the Church teachings are on it in the Catechism, and this is what I found;

"The efforts of the state to curb the spread of behavior harmful to people's rights and to the basic rules of civil society correspond to the requirement of safegaurding the common good. Legitimate public authority has the right and the duty to inflict punishment proportionate to the gravity of the offense. Punishment has the primary aim of redressing the disorder introduced by the offense. When it is willingly accepted by the guilty party, it assumes the value of expiation. Punishment then, in addition to defending public order and protecting people's safety. It has a medicinal purpose: as far as possible, it must contribute to the correction of the guilty party.

Assuming that the guilty party's identity and responsibility have been fully determined, the traditional teaching of the Church does not exclude recourse to the death penalty, if this is the only possible way of effectively defending human lives against the unjust aggressor.
If, however, non-lethal means are sufficient to defend and protect people's safety from the aggressor, authority will limit itself to such means, as these are more in keeping with the concrete conditions of the common good and more in conformity with the dignity of the human person.
Today, in fact, as a consequence of the possibilities which the state has for effectively preventing crime, by rendering one who has committed an offense incapable of doing harm- without definitively taking away from him the possiblilty of redeeming himself - the cases in which the execution of the offender is an absolute necessity 'are very rare, if not practically non-existent."
- C.C.C. (2266-2267)-