Cortez
Tough but Fair
The person on the other horse should have been, more responsible and hacked back with you rather than just gone off ahead of you and then once round the bend trotted off as this will upset most horses. It is not unusual for your horse to want to catch up with a horse that was ahead f them or accelerates away from them. I am sure that a qualified and competent instructor will teach you how to ensure that you have more control of your pony.
Blimey, so not only do you have to ride your own horse, now you have to be responsible for everyone elses. I mean obviously you don't go around endangering other people, oh wait........