how do i tell my family i want to live with my dad?

im 13 years old with a 16 year old sister. our parents are divorced and we live with our mom. we go visit family every summer, but this summer at our dads i noticed how truly happy i am here. at my moms ​​​​​house, neither of us can sleep in our bedrooms due to a terrible bug infestation. here, we have our own beds and a bedroom. theres better living conditions, financial stability, and just overall a better life. i would like to move here, but there is multiple factors making me second guess myself.

firstly, at school, i made it into show choir which ive dreamed of being in for as long as i can think.

secondly, my sister loves her boyfriend more than anything, but shes not allowed to be with him. if we moved, they would never be able to see each other. i fear she would hate me.​​

thirdly, court. i would have to tell a judge all the reasons i wish to move in with my dad, which would mean outing my mom as a neglectful mother. i dont want to get her in trouble because i know she isnt intentionally neglecting us, but intent has no legal sway. she would certainly be locked up, and she would hate me forever. i know this because she already thinks i want to cause harm to her because her DIAGNOSED SCHIZOPHRENIC boyfriend made her think i want to murder her in her sleep. im not playing. so she would think i intentionally got her locked up and i dont want that. i just want whats best for my future.

lastly, i have crippling social anxiety and transferring to a new school would be terrifying! im already a nerd as is, and this is a much bigger school than my small town one. i fear i would get bullied, as someone who isnt afraid to express their love for anime. im also not conventionally attractive by any means and am overweight. im like perfect bait for bullies.​

should i even go through with this? how would i even bring it up?​​​