What can I do to make a point in an argument between my mom and sister-in-law?
What's the point you're trying to make?
I'm pointing out that I'm the only one who's like my sister-in-law, but nobody believes me.
It can be tempting to try to mediate an argument between two family members, but you should only step in as a last resort. Often times people can resolve their own interpersonal conflicts, and when we get involved we can distract from the issues at hand. Trust your mother and sister in law to work things out on their own.
I only want to help and make sure my mom doesn't get hurt.
It's great that you feel protective of you mother, but she's a grown woman who can likely handle herself. If you want to help just stay on the sidelines in case the argument gets out of hand.