It sounds like your friend has already talked to you about her concerns over her daughter's personality and how that has affected their friendships with other people.
Since she opened that door, I think you should have a talk with her, preferably face to face WITHOUT the kids around. Tell her about your concerns - the situation, what happened between the children, how her child reacted, and how SHE handled it. Of course, we all expect children to have their "moments". However if her child is already being aggressive, and is so much bigger than other kids, it sounds like your friend needs to really be on top of her daughter's bad behavior.
Also, in addition to talking with your friend about how SHE is going to handle her daughter's aggressiveness between your children...ask her how YOU can help her when the kids are together. Let her know that you don't want to interfere and don't want to "parent" her child, but that you would like to know how you can help her work to teach the kids how to play together and better handle their disagreements.
Finally, I stand firm with "my house, my rules". So I think that you should also think about what your house rules are when it comes to "not playing nice". Instead of thinking of these rules in terms of HER daughter, think of them for everyone age 1-101...like "no hitting"/keep your hands to yourself, "no yelling/tantruming"/use your words, etc. Then I think you have every right to talk with your friend about your "house rules" and explain that she and her daughter are expected to follow them when in your home.
You didn't mention at all how your friend reacts to or disciplines her daughter when she is being aggressive and domineering? Does she sit in her chair telling her, "We don't do that!", does she tell, does she say, "Oh no, there she goes again", or does she get up out of her seat, talk with her daughter and then make her apologize/give her a timeout/etc?
I think with any child, the grown ups setting the example of what is acceptable behavior (using your words, dealing swiftly with pushing, hitting, etc.), following through with consequences (and not using empty threats) and being consistent are all key.
Overall, I think if this child is hurting your child, then she should have limited chances to behave. If she can't or won't stop being aggressive, then the playdate needs to be over. She needs to understand that HER BEHAVIOR is why the playdate is over. And that she is only welcome back when she can behave. Of course, this needs to come from her mom. But you should feel free to explain to her mother, that you will leave her house if her daughter isn't being nice or is having (another) bad day.