Running away is the worse thing you could possibly do. It will complicate your life in ways you cannot imagine. Not to mention there are predators out there drooling to get their hands on a young girl to control. It's not safe, so please don't.
Frankly I think you're a little young for a boyfriend if that means spending unsupervised time with him. Talking on the phone, talking at school, liking each other - well, that's okay.
Your mom is angry about something and it's not your fault. If she really hated your dad's side of the family, why did she leave you with them to be raised? And - there's worse things than being called an ugly name by your mother. (Maybe she's thinking about how she behaved at 14!)
You can't change how your mother feels, what she says, or how she divides the chores. What you have to change is you expecting MORE from her than she's able or willing to give you. Know this, too - you have every right to love your dad and his family. Sounds like they have earned your love.
But here's the secret: Just don't argue with her. Feel how you do without guilt, love your dad and his family with all your heart, but keep it to yourself. She can't take that away from you.
If you can, talk to your dad and see if there is possibly someplace else for you to live, like with another relative or grand parent. You'll have to be on your best behavior to be taken seriously, and running away would not be considered a smart move just as sneaking around to see your boyfriend would be a mistake.
You may also try talking to a counselor at school and get some advice there.
You are not dying in this life, sweetie, as much as it feels like you are, but you are being seriously challenged with some real problems. I bet you are smart enough and mature enough to look for a way to solve your problems without endangering your life and running away.
Think this through, seek advice from a trusted adult, look for alternate living arrangements, and you'll be making some mature decisions early in life which will serve you well now and later.
God bless you.