She'd be getting more than a tantrum from me if she dared touch my DD. Who knows what my DP would do!! To be honest, I'd lose my shit if I witnessed her grabbing someone else's child, not just my own. But then nothing upsets me more than children being physically disciplined.
When my DD screams in a tantrum (she is 2.5), I tend to just hug her really tight until she calms down. Works really quickly and while she doesn't then (always) get what she wanted, she knows that she is still loved and we are giving her the attention she needs. If we ignore her, she will just keep going on and on.