Both you and your mother feel deeply pained; perhaps the word betrayed isn't too strong, that your brother has married someone who is not Jewish. This is not what you hoped your sibling would do, or model for your own children. Your mother values an intact family and you honored her wishes by attending the intermarriage and brought your kosher food along, as so many of us do under such circumstances, as well. You wish guidance for how to relate to the competing values in your situation, and question exposing your children to something you think is wrong.
In Jewish law there is a principle of b'diavad (advising in advance) and l'hathillah (adjusting to a new reality gracefully, thoughtfully and without being toxic. Just as your mother treasures your brother as more than his marriage choice, so too, do you love him. ? B'diavad, this wasn't permitted, l'hathillah, you have a new fact on the ground, his intermarriage. Punishments in Judaism are up to HaShem, coping with new realities are the province of humans.
While you mention the option to "just be polite to the non-Jewish spouse", I recommend that you get to know her, become a sister to her, let her into your beautiful Jewish life--for his and your mother's sake, if not your own. Have her experience the beauty of Shabbat and chaggim. Your brother made the intermarriage decision--she fell in love with a member of the Jewish people and accepts a place for herself in our family tree---now, her sense of the Jewish people will come from how you treat her in large measure. Creating the potential for hate for Jews in her heart could be a seed you plant with coldness or "just being polite", what wisdom could there be in doing so? She may have talents and a heart for being an aunt to your children that are religion-irrelevant; depriving them of her presence in their lives (after all your brother finds her special, she probably is!) is a lose-lose for everyone. Plant seeds of love for you, your children, Judaism and Jewish people in her experiences with you and you may have good surprises down the path of life.
Breaking up a family by withdrawing contact is a major trauma that creates a tragic pattern in families. It can be hurtful even to your future children. You presumably love your brother in more ways than any marriage could damage, and will care for him and those he loves over time. There can be so much good that transpires when you shift your focus to loving connections by the mitzvah of hakarat hatov, showing gratitude for all that is good in your brother and his family—support the good and be revealed as a good and caring person yourself. All things change—leave room for that possibility. Religious rigidity can damage important future possibilities; also remember, if you realize you don't like her as a person that he and the children will need your support even more. Not all marriages last.
We had your experience in our own family when one family member who is quite frum (religious) announced he was going to cut his sibling off for converting to Christianity some years after intermarrying. When we encouraged him to speak with his Rav, he was surprised to learn the tradition of "sitting shive for someone who intermarries or leaves the fold" is not in Jewish law. Instead he was encouraged to stay in connection with his sibling, to offer to study Torah together, to show caring and to remain a faithful sibling. Twenty years later, she is returning to her Judaism, bringing a bat mitzvah-age daughter in this direction. Thank God, no one shunned or shamed her. (If it's a liberal Jewish wedding, I will attend in the manner you did, if it's a Christian or other religion's wedding, we only go to the reception to be with family but not support the dogma of the other tradition coming into a Jewish home. Rabbi/Priest weddings, are no go for us, children can't choose for themselves, that was a weird idea of the past generation...children deserve to learn and develop inside of a healthy tradition where, however, other religions aren't demonized.)
And what of the issue of modeling to your children? If you live in a frum community, that's done amply. They also need to understand the greater world and be able to navigate that. Self-ghettoizing have serious and growing rates of youth rebellion in our times. You are better served to simply treat your brother and his life with loving inclusion, while emphasizing to G*d willing, your future children, the beautify of two Jews co-creating a Jewish home at times when it is not at all able to be interpreted as disrespect of their uncle.
Should you wish to work through these understandable and difficult feelings via phone consultation, via my non-profit hashpa'ah, Jewish spiritual counseling is available on a sliding scale. with blessings on your life and path, Rabbi Goldie Milgram