Spanking 1 year old?!

Background: I come from an African American Family who believes in spanking kids. I was spanked/hit til I was 18. I am now 23.

My almost 15 month old throws tantrums and falls out on the floor he's been doing this since he was like 3 months. He came out with a "temper" as my mom calls it.

I live with her again due to unfortunate circumstances. I would rather live on the street but its best for my son to live here.

Well here's the issue...

My mom says that I'm too soft on him and that its ridiculous that I let a 1 year old run over me. I have tapped his hands when he's about to touch something dangerous like a hot stove. Often a firm NO works but not lately. My mom says that I need to spank him because if I don't she won't be watching him anymore and no one else will because she says he's bad. I think spankings at 1 are absurd. What would you do? Moving out isn't an option for awhile.