We have a brother who is married to a woman who is nice and friendly when we have seen her, but none of us have a relationship with her because she has walls built around her and will not let any of us in. None of us have been invited to my brother's house in over 30 years, except once. We have come to realize that our brother is pussywhipped.
Mind you, there have been zero arguments and nothing has even happened for our sister-in-law to disconnect from our family.
So, us siblings all decided to have a separate relationship with our brother. We meet just him for dinners and lunches. We invite his whole family to gatherings, as always, and most of the time he comes without her or his children. When I do see her, I kill her with kindness.
So, my advise to you is to contact your brother by beginning a casual relationship through short communication leading up to seeing him over the course of a few month's time, or so. Just a simple text or e-mail is really all you need to get the ball rolling. I would be hesitant to send him a card through the USPS because maybe his wife would intercept it. Whatever you do, do not disrespect his wife and just kill her with kindness.