Matthew 5: 23 : If therefore thou offer thy gift at the altar, and there thou remember that thy brother hath any thing against thee; [24] Leave there thy offering before the altar, and go first to be reconciled to thy brother: and then coming thou shalt offer thy gift. (Sermon on the Mount)

I don't believe I've seen much in Catholic sources about apologizing or asking forgiveness of each other.

Especially with husbands and wives but in other relationships this seems so important.

I've seen a lot about asking God's forgiveness of course, but I can't recall much of anything in the sermons I've heard or catechisms about going and asking forgiveness of one's spouse or children or parents.

Perhaps I just can't recall it...have you seen much on this?

This I do as well because the truth about life is that we all know a lot of dead people. 
You don't know when they won't be here, so it's best to still ask forgiveness and be cordial with people while you have the time to.

I've often tried to make peace in my family by apologizing even when I knew that I wasn't wrong in the arguement or confrontation, just for peace and the sake of the relationships. I'm sorry I did that because it became expected that I was always in the wrong and would always apologize for it. It made the dynamics of the relationships intolerable and further solidified (their) wrong opinions and actions. 
I forgive now but I don't give in- needless to say I don't speak with a few people in my family( they don't speak with me either). I spoke with my priest and he said to just let it ( them ) go and pray for them, which I do. Of course I don't want it to be this way but Jesus said to expect the divisions.