How to build up confidence in singing
Well to start off try this from what I experienced; Well, not wanting to sing in front of your parents is understandable especially if you feel like you are being put on the spot!
My suggestion to you is to take every opportunity to work on your voice ~ even if its just when you get the house to yourself for an hour, have a shower, clean your room etc... Crank the tunes.. or put on your ipod whatever and sing away!!! I used to feel awkward too but now ~ heck, I'll sing anywhere, anytime and I'm really am not shy about it at all anymore... ha ha ha
Although, I dont say it very often on here (dont want to sound like a poser) I sing in a band ~ mostly rock/metal and my best advice would honestly be that you have to work on yourself & your voice.
Once YOU KNOW that you are a good singer it will build your self esteem up! THAT is how you gain the confidence you are looking for. The only way to do that is to Practice Practice Practice.... with or without voice lessons and at every opportunity ;) ;) ;)
or if you have a cuddly toy or barbie, sit them as if its a concert and just SING! TAKE THAT LITTLE RISK THAT SOMEONE MIGHT HEAR YOU! WHO CARES? but if you are really nervous that is a great sign-this shows the adrenalin in you-make some concert tickets for your friends/family and learn a song! THERE WILL BE NO TURNING BACK!!!! And if you just can't do it close your eyes and pretend that you are the only one in the room. pretend that they are asking for you autograph!