Witness45, so if my family trusts in Jesus and that He died for ALL sins and that is our gift from God they will be saved no matter about the gay marriage sin? What if my family doesn't repent? Can they still be saved then?
I understand this topic is difficult for you, they're your family, and you love them.

It's nice to know that you're truly concerned...
What your seeking is assurance in your family's salvation. Let me first of all say, it is not my place to determine whether or not anyone is genuinely saved or not, nor is it anyone's for that matter. Judas traveled with the disciples and Jesus for 3 years, and when the disciples were told by Jesus that one of them was going to betray him, each said "Surely not I Lord; Is it I?". No one suspected Judas. I'm not saying your family is a bunch of Judas's, I'm simply saying that false converts can be found even amongst what would seem like the most highly active and theologically sound people in the world. That's because only God can search the true heart and mind of man. Though we may be able to know many by the fruit of their actions, that unfortunately doesn't mean we can know all. My point in all of this is, you can gain absolute assurance of your own salvation, but assurance of others is a far more difficult task. We can't see inside the heart, but we can see their words and actions. Assurance of others may be difficult due to our inability to see into the heart, but as Jesus said "A good tree does not produce bad fruit, and a bad tree does not produce good fruit." Therefore, it is not impossible to tell if we observe their actions. I unfortunately cannot give you absolute assurance of your family's salvation, but I can help equip you with the tools needed to see between true and false conversions, and how to evangelize specifically to Roman Catholics... I'll try my best...
So in answering your questions above; a person is saved when they feel Godly sorrow for the sins they've committed, acknowledge that Jesus Christ as the Son of God (God incarnate; God in the flesh) and that he died on the cross for our sins, ask Jesus into their hearts to save them from their sins, and then repent and follow him as Lord of their lives...
Repentance isn't a requirement of salvation, it is the product of it. Those who say that they have accepted Jesus into their heart and don't repent, don't truly feel Godly sorrow for the sins they've committed. If they acknowledged their sins as being sinful and wrong, then they would turn away as consequence from them. Many people trip up at the acknowledgement of Jesus as Lord. They can acknowledge him as Savior, but not as Lord of their lives. Therefore they cling to Jesus out of their own selfish ambition (either to go to Heaven, overcome personal obstacles, justify themselves as righteous before men, etc.), and their hearts are not genuinely changed.
Let me put it this way, if you were to tell me you got hit by a mac truck and yet you look and act no differently then if you didn't, I wouldn't believe you. an encounter with something of that magnitude would surely cause a change... So which is bigger, a semi or God? If you truly encounter God, there will be a change. A BIG change.
Now this isn't to say that everything suddenly changes over night. Repentance is like faith in the since that it grows with time. Any true believer is constantly growing in faith as they are in repentance, so don't expect perfect repentance right away, but there should be a rather substantial change to begin with. It doesn't mean they will never fall, it just means they'll never stay down.
So in essence, it doesn't matter that they have some sin about believing in Gay marriage. It's unfortunately the prevailing belief of the time, and therefore they could really honestly believe that what they're doing is right. They may be Catholic because they truly believe it to be the right thing to be. They may very well be sincerely trying to do the right thing. It's good if they are sincere, but you can be sincerely wrong. That's why it's important that they do understand what they are doing wrong in order for them to fix their situation. They can have faith in the one true Jesus, and think that certain actions are right when they're not. But if they truly acknowledge him as Lord they won't for long...