I wouldn’t go to the wedding since your name very pointedly was left off the invitation. But that doesn’t mean your kids can’t or shouldn’t go. Do two teenagers really need parental supervision at a family event? (And if so, why??) Won’t there be other adult family members who can keep an eye on them (and maybe even pick them up and drop them off) — grandparents, another uncle or aunt, an older cousin? If there’s no one you trust to supervise your kids, you’ll need to assess whether you can trust them on their own at the wedding and talk with them about any rules you might have for them to follow while they’re (temporarily) out of your care, as well as what time you’ll be picking them up (or arranging for them to get home).
I’m confused. If your wife converted to Judaism, why is she attending Catholic church regularly? Why is she responsible for teaching and sharing Catholic traditions? Did you not agree before you got married or had children what faith you would raise your children in? If you agreed on Judaism as the family religion but your wife feels like you aren’t doing enough to expose and teach your kids about Judaism, you need to re-visit whatever earlier discussions you had about how to raise your kids, explain how important it is to you that they are raised with the foundation of Jewish traditions and beliefs, and then start walking the walk.
It’s one thing to say you want your kids to have certain traditions, but, if you aren’t doing anything to expose them to those traditions, I can understand why your wife, who wants them to have some religious foundation, would fall back on the religion she is most knowledgeable and comfortable in (though I’m still confused as to why she converted if she wasn’t willing to give up Catholicism). At any rate, you need to sit down and discuss things with your wife. Since you seem to want Judaism to be the dominant family religion, what is it your wife needs from you to (re?-)agree to that?
If you have a relationship/dating question I can help answer, you can send me your letters at email@example.com.