I agree that this is probably a hierarchy problem and the 2year old is winning.
You have made a big mistake in purchasing two young horses when you say you are a novice -as the saying goes "Green +green = black and blue!"
It takes years of experience to train a horse correctly. If you do not know what you are doing, and it is all very well having a trainer there with you, how can you teach a young horse what is required when you do not know the 'feel' you are trying to achieve?
You can liken it to someone who has only driven on rural roads trying to teach a non driver how to drive a semi in New York City.
You need to learn how to handle both horses on the ground, to read their body language, to correct the slightest issue and to take hours of lessons on a schooled horse.