Wording for ceremony only student invite?

Does the school or church send out newsletters? Could the newsletter note when your wedding will be?

If the program regularly sends out emails for special events, I'd probably just go that route with something like:

Dear Sunday School families,

Our dear Sunday School teacher Ms. Ada Smith and her fiance, Mr. Michael Jones, invite you and your child(ren) to attend their wedding ceremony on Saturday, November 1, 2019, at 2 p.m., in the church sanctuary.

If you can swing it, I might do a quick cupcake or cookie & punch "reception" immediately following the ceremony for the kids and their parents. Or, if that doesn't really work with your timeline and/or budget, maybe prepare a small edible "favor" that someone (a fellow Sunday School teacher?) can distribute to the children as they leave the ceremony. (For daughter's wedding, we made favors with two large Costco chocolate chip cookies [daughter & SIL's favorite dessert], in 4" cellophane treat bags we bought at Michael's, and custom stickers that said "Thank you for sharing in our day! Love, Mr. & Mrs. Adams," with their wedding logo. They were probably less than 75 cents a piece to make, and there were none left at the end of the night.)

I wouldn't invite people to my wedding if I couldn't also invite them to my reception. And inviting 20 kids, plus their necessary parents, is going to throw your guest list off wildly.

Your wedding is not an educational experience for your students.

Churches are generally open to members. The kids do not need an invite to come. I did suggest the church send the announcement.

At the house of worship I attend the wedding ceremony is not a private by invite only

I'd second what MOB So Cal said up there except should you maybe add "adult only closed reception to follow" or just "closed reception to follow" ? I have no idea but that's just a suggestion.