How do I convince my mom to let me move with my dad to Idaho?

Background Information:

My parents are divorced and have been since the summer of 2011. I live with my 7 year old little sister and my mother at my aunts house in Washington (state). Both of my parents are homeless. My mom lives with her sister and my dad lives in the living room of a 2 bedroom apartment with 2 roommates (also in Washington about a 45 minute drive away). My sister and I see my dad every other weekend and some holidays every other year.

Problem:

I get along with both of my parents very well in different ways, but lately I’ve been thinking of moving to (Moscow) Idaho with my dad. My mom said that if my little sister came with me she would be fine because she does not want us to be separated. My dad was of course totally fine with it but he even told me that my mom would not give up both kids. He says that I’m old enough (14 years old) to make my own decisions and that Victoria (my sister) should be able to say where she wants to live. I asked my little sister what she thought about moving and showed her the house (One that we would have to our selves) we would live in and she was up for the idea. She told my mom that she wanted to move with us and although I wasn’t there for the whole conversation I over heard a few things.. My mom convinced my sister to stay by making her feel bad. My mother is very ‘passive aggressive’ (1 reason I would like to get away from her) and told my sister things like, “You’re going to cry every night if you go. Why would you make a stupid decision like that?” “If you go I’m going to be crying all the time, I’m going to miss you so much.” “I just want to make everyone happy. If you think you’ll be happy then fine I wont stop you.” And when my sister gave in my mom said things like “By law you aren’t even allowed to go.” When you are both 18 you can go do whatever you want, but I’m not letting my kids go anywhere until then.” Hearing all of this makes me want to go even more. I knew Victoria wanted to stay with her mommy anyways and I think its for the best. I know that If I talk to my mom about it, she wont let me go. It’s just going to create an argument that I wont win because of how sensitive and empathetic I am. I know it’ll hurt her if I go and I wont be able to argue with her when she eventually starts crying. I hate that she uses my feelings against me. How do you think I can make her come to her senses and convince her that it’ll make me happy? Should I write a letter? Or tell her straight up and try to win an argument? Trying to just ‘Tell her how I feel’ Isn’t going to work and I already know that.

Why I want to move:

• My little sister and I fight a lot at home and if we split I feel like we would be closer. ‘Distance makes the heart fonder’
• When living with my dad I feel as if I will have more chances to be more independent, learn new things, and be open to new experiences.
• I miss having my own place to live. Somewhere where I can actually call home and be myself at. I’m also at an age where I think I could really use a new room instead of sharing with a 7 year old or sleeping on the living room floor/couch.
• I hate the place I’m living. I want to go to the country side and just get out of the city. I hate the school and the weather and absolutely everything. I want to start over in a new place and at a new school. I want to make new friends and create new memories.

I love my mom very much as well as my sister and dad, but I’m just not happy here. How do I tell my mom this? Can I really not leave with my dad by law? I cry every night just thinking about it. I know I probably wont be able to help it but don’t want to hurt my mom, friends, and/or family but I’m just not happy here… What can I do? What should I say?

Sorry for all of that typing^^ lol -Thanks.