My mom has wants my toddler to call this bum Grandpa, how do I deal with this?

You are the parent. Who gives a sh it what your mum says. Very simple. Tell her not to tell your child to call him that. Tell your child he is not your grampa. Easy. If your mum fights against it cut her off from contact until she acts right.

From the sounds of it, this man is not your BD, just a boyfriend of your mom, right? So he's not biologically or emotionally related to you. Your mom, however, is a different story. You may not be very fond of her in this season of your life, but she'll always be your mother and there's a good possibility you'll have a better relationship in the future. Have you thought of explaining to her that you value your relationship with her, and as a parent, you want the best future for your child, which means presenting positive role models to him? Family should especially be positive, and being given the title of Grandpa is an honor. You can soften this by sharing some of the reasons you respect and love HER. Even if this list for your mom is a struggle to make, you can probably think of a few things you can encourage her in, right? Doing that may make it easier for her to understand why you're opposed to this guy being "family." Best of luck to you!

You have to stand up to her and tell there is no way he is ever going to call him Grandpa. If it makes her mad, so be it.