Dear Gina,  

I am not sure if your family is ashamed. You don't tell me if they are practicing Catholics, and that would matter.  

Here are some alternatives for you to consider:  

You are only 14, you do sound like you have a stubborn streak, and you already (from what you say) have made your mistakes. I would guess you were pretty rebelous then too. So maybe your parents think that this is just another of your ideas to go against them. Or it may be they are not sure about the change you have made, if it is complete. Or they may think that with your character you would not fit into consecrated life. Or they may think it is just a phase you are going through, that it will wear off and they don't want you to do something rash right now.  

Now, what can you do? First of all you have to get closer and closer to Christ. Your ambition to serve God alone is good, you now have to mature in it. Get to know Christ, spend time each day in prayer (pray the Rosary, especially), go to Mass and Communion as often as you can.  

At home you will have to be your best, helping out, doing your studies, etc.  

Then you have to do something for others. For example, do something for younger kids, help with CCD, or visit the sick, or speak to your pastor and get something going for girls of your age in your parish (a club, choir, Christian Life group, help in the youth work, etc...). 

If your parents are not practicing Catholics and do not understand their faith, you will have to pray for them and let your actions convince them.  

God bless.