Your question pushes us straight to the center of the tension between Judaism as an exclusive tribe with some inherited “birthright” component (with ongoing debates about patriliniality/matrilineality), and Judaism as a practice and belief system open to any and all.
You should know that there are now Jewish communities that will welcome people who want to participate, without litmus tests for parentage or a dissection of who converted when and how. These communities are saying, if you want to be Jewish, come be Jewish with us. Personally, I see this as practical, at a time when millennials are disappearing from the pews of both churches and synagogues. I also see it as spiritually inspiring.
On the other hand, if your son wants to join a more traditional Jewish community, he will need to document your mother’s Judaism. That will mean pressing her for details on whether and when and how she (or her mother or grandmother) converted. While this may be painful for your mother, she will need to understand how this information affects you. Depending on whether you can document clear answers, and what those answers are, you and/or your son might need to convert through a particular process to satisfy the membership requirements of a particular Jewish movement.
It will be emotionally difficult if you discover that you are not considered Jewish in some communities, after growing up practicing Judaism and believing you are Jewish. While yours may be an extreme case, all of us who are “patrilineal” Jewish offspring have had to process this realization. Some make their peace with the necessity of converting in order to align their experienced identity with membership requirements of a particular Jewish movement. Some have left Judaism in frustration. And some of us find or create Jewish communities that welcome us as we are, working to help people stay connected to Judaism in a 21st century marked by complex religious identities, widespread interfaith marriage and heritage, and a shift away from exclusive to inclusive community-building.
Susan Katz Miller is both an adult interfaith child, and an interfaith parent. She is a former Newsweek reporter, and the author of “Being Both: Embracing Two Religions in One Interfaith Family” (Beacon Press).