persuade singing lessons?

I really want to take singing lessons but my parents said no. Reasons
are because:
1) We don't have that much money (I take violin/piano lessons, my
sister a science class and piano lessons, my brother
piano/drums/swimming lessons)
2) They don't THINK I'm devoted enuff to practice (because I can be
quite shy)
3) Whats the point of learning how to sing unless you're gonna become
a musician (which they highly doubt and only made me take instrumental
lessons for a hobby)
4) My grades in school are high but Im in the lower classes -.-

Reasons why I want To:
1) A musician is what I have the best chance at considering I suck at
school (but I wouldn't dare say this to my parents as they will
definitely reject it)
2) I want to learn how to be a good singer cuz I enjoy music.
3) I am willingly to be devoted enough, (thinking about asking them
everyday until they agree, or is that a bad idea?)
4) It will help my self confidence which is really low right now (If
you weren't my friend you'd have to be at a a foot or less to hear me
talk, and my friends never heard me sing even though they stand right
next to me, I ALWAYS mess up on violin recitals because I'm too
nervous)
5) It could help my piano practical aural tests which considers
singing.
6) I Realllllllllly want to do it and if they said yes it'd make me
happy.
7) (Oh and I'm a bad singer which is why I want to take lessons, not
bad but not moderate either -.-

So as you see, I have more reasons although my parents have more
strong reasons. Can anyone help me say something to persuade them?
(Also, *sigh if you want you can persuade me NOT to take lessons but
that could be very hard)

P.S. I'm only 13 and I want to learn as much as possible before I grow
up. (going off to ask my parents again, most of the time these talks
ended up making me depressed because my parents emphasized my poor
grades, my poor devotion, (I only practice piano 30 minutes even
though I've been playing for almost 7 years, and violin for 15 minutes
(I know that hardly anything) when I've been playing for 4 years, and
I spend almost 15 hours on the iphone a day, 5 hours to sleep, and 4
hours to shower, brush my teeth, eat, practice, etc.) and my poor
skills. ( I actually think I'm not that bad at piano/violin but they
always compare me to my sister which is unfair since she is 2 years
older then I am altthough my piano teacher thinks she might've been
more advance then I am at my age and my parents only think about
grades in which she is in the advance advance classes while I am in
the normal classes but the norm for students here usually take advance
classes.)

Sorry I made the situation a a little hard to persuade my parents with
but any suggestions to so with my schedule, devotion, persuading, etc.
would be appreciated. Sorrry again for writing so much, I have alot of
anger and self pitying I need to express. :P