Raising Jew-ish kids

My Jewish heritage is extremely important to me. I went to Sunday school and Hebrew school growing up at a Conservative temple and was Bat Mitzvahed. Always observed and celebrated the holidays. Post Bat Mitzvah I didn’t have interest in attending synogogue but the traditions and holidays remained. I identify as a cultural Jew and do not consider myself religious. I’m agnostic.

Now I’m a mom of two young kids (with a non-Jewish husband) and want to raise my kids as proud Jews (I’ve always felt this way but especially within the last few years). It’s hard to separate the culture/traditions from the religion of it all, but if I don’t put my kids in religious/Hebrew school, I worry they just won’t identify as Jewish. I’m leaning towards doing it, but wanted to hear if others have felt this way. Do I just suck it up, expose them to all of the teachings/God stuff and also return to synogogue? Husband is supportive and accepts whatever I decide.

It’s a tricky way to feel!