As both a longtime preschool teacher, childcare provider and parent, this is a situation I've seen a lot of. Even in my personal life, I've had to face up to the fact that some of my friends and I parent in remotely different ways, and cope with how to choose what is best (not always popular) for my son.
It sounds like what you are doing to help your son is exactly what we teachers would step in to do. Sitting next to your child, helping them when they need help with their interactions, and having an realistic understanding of your three-year-old's self-regulation/impulse control (and perhaps, clumsiness) are all on par with what your little one needs. He may be bigger, but he's still a little one. It sounds like you are doing an excellent job.
The differences between your parenting styles is a conversation best broached when your children aren't engaged. Or, if she seems insensitive to your concern, a letter would be another route to take. I think it's important to address, but not in front of the kids.
If it were me, I would start by acknowledging the age difference between the kids and her concern for her son's safety, which is appropriate. I would then tell her how it feels for me, as the parent of the older child, to have my child yelled at. I'd also remind her that children often listen better to directions when they aren't startled or scared, and that I'd like my son to have a trusting relationship with her; that raising her voice will only scare him.
I'd then mention what I would like her to do when something happens. Say, if the older child were hitting, etc, for her to say "Stop." or "Here, you can play with this" or something positively redirective. If she didn't feel comfortable with it (or says "That won't work), then it probably isn't within her range of parenting skills, and she could ask you to step in or she could pick her toddler up.
Never, ever, should anyone touch a child in a rough, angry way. Make that perfectly clear and do not tolerate it.
Just my opinion, but I would keep your son with you when you leave the room and would not leave your child with this person who seems to have a hard time controlling their temper. Parenting skills are often hard won and have to be actively pursued. Some people will try to learn gentle ways of discipline, and some won't. It's up to us as parents to decide how much we want to expose our kids to. And, for what it's worth, we adults have an idea that kids at the ripe old age of three of have "friends"...not so much, it's more that they have playmates who later become friends.
Best wishes however you proceed.