I hear a couple different things here, so I will approach them 1 at a time.
First, your girl...
News flash: ready? She's 3.
3 year olds don't know much about anything, let alone how to effectively defend themselves to a bully. So that's where parents come in. Most adults don't even know how to effectively handle a bully. She likely can't even remember what you've told her about what to do because it's based on concepts that are beyond her.
So at this point, I'd be less concerned about teaching her dependence upon mom to fix her problems than I would be about her general well being. As a father of 5, I've learned that even the crappy situations have to be prioritized. No, you don't want her to learn the wrong lessons, but her personal safety is more important. And at 3, you're not really teaching her much on dependence anyway.
Second, you're both dealing with bullies.
Read this then come back. I like my answer. The rest of my answer here will take into account the context of my answer in that thread mainly because I believe that it applies here.
See, bullies hold a special place in my heart because they are willfully misunderstood. And I take no small amount of pleasure in busting their groove by informing people that their take on bullies flies in the face of what they know to be true.
Most people's solutions to bullying involve either changing the target (themselves, whoever) to avoid inciting the wrath of the bully, OR some level of hope that they will see reason and an appeal to sensibility will work. In my experience, I have found these methods to be 100% ineffective.
In other words, you already know who you're dealing with and what her reaction will be -- The other mother is fully aware of the problem and has chosen to do nothing -- yet you hope that a plea for sanity will work; yet you hope, you're crossing your fingers, that the next soft appeal for a little sensetivity to your baby's feelings will work.
So here's another news flash and a little tough love: It won't work. Your daughter will wind up crying, you'll wind up crying out of frustration, the other mother won't care and nobody else will say anything. But I'll bet you already thought of this... willful misunderstanding.
(Side note here: she sounds exactly like the little 6th grade girl who justified her bullying of my 12 yo daughter "I'm just preparing you for what will be coming. There will always be someone older picking on you.")
To confront the mother...
I would advise that you don't worry about being nice. But that doesn't mean be a jerk either... just push nice down down down the list of priorities. If the mother is as generally adversarial as you describe, there will be sparks no matter how you approach it, so keep it simple, direct, free of expletives, but stern and solid. Yes, it will be difficult because as adults we're conditioned to 'get along' and I hear a lot of "getting along" from you in your post. It's very difficult to jump from that track into the oncoming traffic of "aggressive issue resolution".
Therefore, here's my attempt to give you a little energy towards dealing with it. You wondered how she would be if it was her kid on the receiving end? Well how about putting her on the receiving end...
"That's the Xth time in as many get-togethers that your child has done something to physically hurt my child. I'm asking you plainly: please make it stop. Or is it just OK to allow your kid to hurt the others.
It's a social group with a host. Take that opportunity to ask the host if it's ok with her. Ask the other parents right then and there. A public confrontation with a flash opinion poll. And you will see exactly who you're dealing with. (I mean this in several different ways and i'm curious what the results are.)
Be mentally prepared for attempts to deflect or derail. Verbal volley ball "well they're tired because you were late" kinda thing. Stay on target... because an idiot will drag you down to their level and beat you with experience.
"none of that has anything to do with your kid hurting mine and you refusing to do anything about it."
It's going to be a difficult scenario for you, but that's nothing that a little practice can't change. Practice the altercation. Consider eventualities. Practice reactions. Talk to yourself in the car (No really, do this. It's ok, laughing truckers don't matter). Allow it to make you angry. A parent's anger can be a force for good when channeled into defending their child.
Above all else, understand that you're not teaching your 3 yo much of anything with this interaction... you are teaching yourself how to defend your child when you believe they need it. Trust me, you won't regret it.
