I understand the emotional responses but being just as or dirtier than the catcher is lame.
These are high school aged kids, or close to it. Are you as a parent really going to go on the field and fight a high school kid? I hope not. As a coach are you really going to instruct a kid to try to injure another kid....I hope the F not. For two reasons. First, it makes you a total scum bag. An adult who cannot keep their emotions in check and sends a kid to do their dirty work should not be coaching or working with kids. Secondly, what if the girl ends up being seriously injured. The kid you sent out to do the dirty work has to live with that.
A parent going on the field is going to be banned from any further games, so, not only are you seriously embarrassing your kid you will not be able to see them play anymore for their school (assuming this is high school).
The players will usually work this out on their own on the field anyway.
As I said before, if the coach of the catchers team was any good she would be getting benched whether this was on purpose or not. I have pulled guys when I was coaching youth football because they couldn't keep their crap together and would get too angry.