I can see that previous expert has opted out.so, I would like to answer the question.
In this answer I consciously concentrate on the practical aspects of you able to resolve the situation and help them when you will discuss with them next week.
As you rightly put, sometime both might be good but might not get along with each other. The reasons could be due to different personalities, low threshold of misunderstanding and sometimes pride getting in the way to Apologize which helps to move on.
When you discuss with them it is important you have a mind map how you are going to discuss the core issue and resolve in a positive way where both feel Win-win situation.
Firstly, it is important for you to listen from both sides before making any judgments. They should feel that you have taken their account seriously.
You set out the fact that you love them both equally and you would do your best to help them to understand things.
You start the discussion after hearing their version and start with an objective of separating the person from the problem. By separating the problem from the person, real issues can be debated without damaging the relationships. You would be quite amazed to see the difference in their attitude if it properly done.
Then start with the agreements first. For example, my guess is both would say they Love you and like you. Both would say they got along well up to certain age and like some aspects of each other. By this, the animosity would become slightly less to a point further discussion might be helpful.
Then start by asking them to look at minor issues and explore further how they can look at that difference. Try to concentrate one thing at a time. Ask them not to target one another rather try to see the positive side in another or imagine to place themselves in others shoe before they become critical towards other.
By the fact that they both are 19 years tell us that they both might be busy in their lives,have lot on their plate in the form of balancing education/work with relationships and also other stressors. So, sometimes people in that situation feel it is easy to get upset or critical to a person well Known to them like a family member to ventilate their stress
or frustration because they might take things granted with family.so, it might be helpful to explore this and if they are doing this subconsciously then try to help them to tease out their stressors and seek help or deal with stress by different methods which are more helpful, for example by being close to each other.
I know it must be difficult for you to see them like this But one thing you can not do is being complacent and wait for the issue to resolve by itself because most often it won't unless addressed pro actively.
I wish you all the best.
Please do not hesitate to ask me if yo require more information.