Accusations, and separation from my siblings

I have an older brother, little sister, and a little brother.

23,14, and 7.

But I've never met them until 10 months ago, because I was away in a different country for 9 years (I'm 19 now).

I tried to connect with my little sister.

Texted her, got to know her, we spent some time playing her games.

One day, I got her a gift on her birthday.

My mom found out, she insulted me, kept calling me names, accused me of having romantic feelings to my own little sister, made her block me and cut off our connection.

She told her that it's inappropriate to be around me, even if we're siblings.

Now my little sister is always anxious around me, never initiates, treats me like a stranger.

I moved on, focused more on my little brother.

I have a ps4, I thought of a good way to allow him to play on it, which is using the reward system.

Started small, just a few English words and he can play.

He was okay with it, then he got bored and started complaining.

Our mom found out, and instead of asking me anything, she accused me of hurting and teasing him, told him that I'm stingy and cruel.

Instead of discussing a healthy method with me, she insults and accused me of being mean to him.

She took him away to live somewhere else with his aunt just because I'm not satisfying him every time he wants to play on something he doesn't own..

And she gives him her phone 24/7, he does nothing but playing endlessly from morning to next morning.

But I get told that I'm cruel for trying to do something that will help him.

My older brother is on her side, he doesn't even ask for my side or discuss anything, he accuses me just like her without listening.

What do I do?

They're the only people I have in my life.

Friends and girlfriends would never fill that hole that only they can.