Shalom and thank you for turning to us. It is indeed sad to hear about friction in the family. It sounds like you are a sincere and sensitive family, and you are a caring sibling. So what in fact can be done about the disturbing situation you describe?
From your description it is possible that there is a factor here that has not been shared with you by your brothers. Something that would shed light on the situation. Of course, you cannot ask for clarification since this would be perceived as prying or simply bothersome. The geographical distances you describe also do not help, at least in a sense.
Truthfully, there is little you can do DIRECTLY to alter the situation, but there are MANY things that can be done indirectly that can influence it, ranging from the practical to the more directly spiritual. There is a custom to say the chapter of Tehillim that corresponds to a person’s age. If you are 30 for example, you say chapter 31 for yourself and if you are praying for someone else, who is 36 let’s say, you recite chapter 37. G-d hears our prayers and a small consistent investment like that will certainly have a positive effect, even if you are not aware of it. This tip is in the category of belief. Belief in Hebrew is אמונה, ’emunah’. This comes from the root ‘imun’ which means practice. That is why a small consistent investment is a good approach.
This brings us to trust in G-d. The Lubavitcher Rebbe, Rabbi Menachem Mendel Shneerson, strongly recommends learning the section on trust – ‘bitachon’ in the ethical work called ‘Chovot haLevavot’. If you search you may find it in English. This is something that you can invite one of your brothers to learn with you without any connection to ‘the situation’. You can just say you were told its very interesting and powerful and would he like to learn with you, on the phone or on the computer. We live in a small digital world. It may even be possible to involve them both. Learning Torah brings the hearts closer. If only one brother wants to participate however, or even neither of them, YOUR trust will be strengthened. You can learn it by yourself or with a friend or a different family member.
These above-mentioned steps will strengthen you and when you are strengthened it has an affect on others.
Speaking of which – you do not mention if you yourself are married? It is important to work on your own immediate family unit. Whether you are at home with parents, or you are married and living in your own home, your focus on that immediate surrounding to make it a better and more illuminated place, has a spiritual influence on the rest of the Jewish nation. In the basic text of Chassidic teaching, the book of Tanya, Rabbi Shneur Zalman of Liadi, the author, points out that according to Kabbala we are all children of One Father. This is in chapter 32, לב in Hebrew. This is no coincidence, since לב means ‘lev’, heart. Chapter 32 concerns the matter of Ahavat Yisrael, loving your fellow Jew. This is what you are trying to do and have others do. Realizing that truthfully our souls are all connected – like one entity, because we are all children of the same Father, can strengthen us. It means indeed that the efforts we make in our OWN ‘four cubits’ – in other words our own daily lives, can affect others even though they are at a physical distance.
You also do not write whether or not there are parents in the picture. If it is possible to make family get togethers from time to time, this could be a practical way to bring the brothers together. If you are not yet married and you find your ‘bashert/e’ – your designated partner, this may stimulate your single brother to do so and then he may follow suit and find fulfillment… which would possibly improve the situation. It is a positive thing to utilize the service of sincere and well recommended match-makers.
In Tehillim 16:8 it says “I have placed the L-rd before me constantly; because He is at my right hand, I shall not falter.” In the merit of your focusing on what G-d wants from you in your personal life, you gain strength and stability, and the next verse continues: “Therefore my heart rejoiced and my soul was glad…” – with G-d’s help you will hear good news!
Sometimes challenging circumstances can work themselves out without any intervention, and there is a possibility that it is not as negative a situation as it seems. In any event, our recommendation is to have patience, believe and trust in G-d, and build your own spiritual life, which has a cosmic influence! Wishing you much success!