It is a basic part of being well-mannered for a horse to NOT squeal, strike out, turn and kick, etc when handlers are present. When horses are loose, they are on their time. When I am around, they are on my time and better demonstrate good manners at all times.
If it had been me, I first would have positioned myself to one side and not directly in front of either horse. Then, when it squealed, I would have yelled loudly at the horse and aggressively stepped toward it and waved an arm in its face -- regardless of what the other handler did. As a matter of fact, I will frequently say a firm "Ah!" when someone approaches with a strange horse, either ridden or led. It will put most horses unknown to you in a more inquisitive mode and less aggressive one. It will serve to do the same for my horse. If you do this, almost any horse with ears back or half-back will bring their ears forward and look at you in a much more cautious way. They will not just wade in and act aggressively like you are not there. I can put almost any horse on notice that they should tread lightly and be cautious when they approach me.