Well, it’s my mother’s FATHER side. It gets damned complicated, doesn’t it?? I just sometimes feel that my ancestors are calling out to me to come home. I’ve felt this way for several years now - as did my mother.
OK, so by Orthodox rules your mom was gentile and couldn’t have passed the race down to you unless she converted explicitly to Judaism before you were born. Reform and Conservative would be easier in their process. The Sephardim are like liberal Orthodox in their approach.
It’s only fair to note, however, that if you hark clear back to biblical times, you see that the Christian church sprang off of the Jewish people. It was decades later, when it began to see significant opprobrium in the synagogues (this guy Jesus went around talking like he’s God! and he even seems to be death-proof! what the hey? the rabbis never prepared us for this!), the church began embracing gentiles in widespread numbers. Your family might disagree among itself, but it ends up being God you have to look for. IMHO, and at least it’s logical.