My mom is the same way, and she insists on not using brown sugar in her ribs. As a result, her bbq is often dry, salty, acrid, and too smoky.
You don't need brown sugar to make sweet meat. Brown sugar is used to balance out the flavors of the salt, the smoke, the pepper, and it ties all the aromatics together. Sugar is also what develops the "bark", or the outer char on smoked meat. You should incorporate brown sugar into your rub because the best rubs won't taste sweet, but the worst ones won't have sugar.
Get it?
Start with salt, then mix about 1/5 of your salt quantity as dark brown sugar. Then build from there with paprika, onion powder, garlic powder, and fresh ground pepper. I've never measured my rubs, but have always started with salt & sugar. None of my BBQ is ever sweet.