Susan, I've been in this situation: my brother married a woman with children, and he asked me specifically to act as a big sister to her daughter, which I did because I grew to love them all very quickly. SIL was wonderful to me, the sister I never had. Fast forward a few years (not 20, but about 7 or 8), brother and SIL are embroiled in a horribly nasty divorce, my brother the one completely at fault, SIL crying on my shoulder over all of it. Now, my brother and I have never gotten along well, and he totally freaked out when he found out DH and I were still in contact with her (dinners, phone calls, emails). We couldn't imagine how we could cut her and the kids out of our lives just like that, but he said I should have chosen blood over water, etc, and to this day he has never forgiven me for this "betrayal." As it turned out, a short time later, SIL decided she needed to sever all ties with my family in order to heal after the divorce, so I lost her anyway. And as I mentioned, my brother has held an enormous grudge against me years later over this issue.
Not saying your mother is like that, but your brother may want to weigh his options a little and think about what future repercussions could be and what it's all worth to him to keep contact with him when your mother is so against it (all the while agreeing that she's being unreasonable)...
"There are times when we're dirt broke, hungry, and freezing, and I ask myself, why the hell am I still living here? And then they call. And I remember." ~Mark, Rent