My younger brother(poa) and his wife (someone mom reaaly trusts and loves) and I (live 90 minutes away) are struggling on how to include/not be resentful of brother who lives at quite a distance, has younger kinds than we do, still in hs, and who does not drop all and show up when mom is hospitalized. I understand this, poa brother is resentful. Trying to get everyone to have a job and get along any advice?
What your brother could do would be to send your POA brother (and you) some kind of regular R&R gifts (if he/you would appreciate it) like massage certificates or dining out certificates or movie tickets for him and his wife. Or offer to pay for a weekend getaway, something like that where he's acknowledging the effort and stress on his brother.
The most I get out of my brother is when he sends candy to my mom and tells me to "get my fair share" of it. UGH. Ticks me off every time he's done that. Regular thank you cards would also be appreciated from my perspective. I don't get those either (ever). :)
Here is what I think: You are not responsible for all the relationships in the family. Do your best to get along with your Near Brother and your Far Brother. If you see some things NB could do to help out, it would be thoughtful of you to share that with him. But the relationship between the brothers is not your affair.
Far brother could call Mother regularly, if she is able to handle phone calls. (My mother cannot.) He could send cards often. (My mother loves that.) He could let NB know that he appreciates all of NB's hard work. (Maybe you could suggest this, in a totally non-confrontational way.) Maybe some simple things would lighten the charged air bit. Or maybe not. Maybe the relationship between your brothers has always been complex and ambiguous. Maybe there are elements of it you know nothing about. Maybe FB has problems with his relationship to your mother and is glad to be too far away to be involved.
You can try reasonable suggestions in a conversational way. But then just focus on your own relationships with all the people involved.