It sounds as though you're being shut out for trying to see both sides and have an opinion. Often, when couples split, there is a small chance of reconcilliation. However, now and again, one person is adamant that it's over and once they've made that decision, it's final and they do not wish to discuss. Whether that's through guilt or simply because they've allowed the relationship to get to a point where they seriously dislike their spouse, who knows?
It sounds as though your father sees you as an adult who should accept that these things happen without having to get involved. It's great that you support your Mum but perhaps that's something you should do privately and keep any conversations/opinions etc. away from the Father and Brothers.
I get the impression that, whilst you're trying very hard not to take sides (good for you), deep down you do feel as though your Father was in the wrong. This may well be the case and you're obviously going to be hurt yourself. Sometimes our feelings come through, no matter how hard we try to hide them and I suspect your Father has trouble dealing with that.
Look on the positive side - if your Father couldn't care less about you, your brother(s) wouldn't be behaving in this way. Brother number 1 is obviously defending the Father - so the bridges are still there to be built on.
How much do you want them to be a part of your life? You could write another letter. No ultimatums though (your councellor shouldn't have advised you to do this). Just explain that you've had a tough time but would like to put it all in the past. Guilty people don't deal with demands or ultimatums well.........they often relieve some of the guilt and give them the perfect opportunity to turn the situation around and make you feel like crap........which I think you do.
Good Luck