I know the default is to be cordial when I meet her and give her the benefit of the doubt, but how do I handle it if she puts him down in my presence?
For the former I recommend, yes, the benefit of the doubt. But you can’t half-heart it, or else you’ll take the slightest of her transgressions as license to believe the worst.
So try looking at yourself through this lens for a moment. Page through your memories of raising your daughter, and fix on a couple of your lowest moments. Times you yelled, times you acted selfishly, times you said something mean. Now imagine your daughter spinning these tales for a therapist. Yikes.
You may know these were deeply regretted exceptions, typical and human and duly mended, but you also need to know that, if phrased just-so to someone who wasn’t there and doesn’t know you, these could paint a scary picture of you. Of anyone.
When you meet the boyfriend’s mom with that in mind, maybe you can upgrade your we’ll-just-see to a truly open mind. Think of it as innocence until she proves herself guilty.
As for any mistreatment you witness, handle it as you would any other: Stick up for the target. Anything from a raised eyebrow to a full-out “I believe you owe X an apology” can let people know unkindness is unwelcome here.
But this isn’t about etiquette.
She, meanwhile, is trying to have a say in what you think and feel, which is a boundary violation. It’s also bad for a relationship. For that matter, so is the aural cheese-grater that is a speakerphone.
Usually the best way to handle behavior as boorish as hers, since the chances are slim that she confines it to phone-bombing, is not to take it anymore. If you’re not there yet, then change your own behavior: “Hi everyone! Girlfriend, call me back when you’re free,” click. That puts you fully in charge of what’s fully yours to control.