Arthur Miller's The Crucible is the story of the Salem Witch Trials, of course, but it is also a story of trial and testing for many of the characters. A crucible is a great test, and from your question you seem to understand that John Proctor finds himself in the position of making a choice to live or to die--probably the most significant choice a man must ever make. Your question implies that he chose to protect his reputation (a rather selfish choice) over staying alive for the sake of his family (the more selfless choice); however, I would assert that Proctor chose to die with honor as much or more for his family as himself.
It is true that he receives personal redemption when he ultimately chooses not to sign his name to a lie. The other thing that happens, though, is that he has set himself up as an example for his sons to follow. His final act is honorable in every way--he neither lies about his own actions nor accuses others in an attempt to save his own life. He says he must do what is right to save his own soul, and what better lesson can a father teach his sons? If he had made the other choice--to lie and accuse others of witchcraft--he would have been teaching his sons to be cowards.
In the end, then, John Proctor did both of the things you mention in your question: he saved his reputation while fulfilling his obligation as a godly mentor to his sons.
This is really a good question. I believe John Proctor was justified in maintaining his reputation. A good name is something to strive to keep. A good name is worth more than gold:
1A GOOD name is rather to be chosen than great riches, and loving favour rather than silver and gold.
You can't put a price on a good name. No doubt, John Proctor loved his family, but he could not give up his good name. That is all that he has that is of value.
Even Elizabeth, his wife, claimed that John had found his goodness and she would not take that away from him:
The play ends with the final statement from Elizabeth: “He have his goodness now. God forbid I take it from him!”
If Elizabeth feels John has done the right thing, he must be commended for maintaining his reputation. I respect John for maintaining his reputation. He maintained his integrity. He claimed to be innocent of witchcraft even in the face of death. He did not live and die in vain. He will be remembered for not giving in to a corrupt court system. He could not claim to be involved in witchcraft when in fact he was not. Honesty is the best policy, even if it means death.