My mum got married without inviting me. She didn’t really elope. It wasn’t like a surprise as such. They had a small wedding with friends only and no family. She purposely only told me a week before because she knew it would be impossible for me to travel on such short notice, we live in different countries and I was pregnant at the time.
Honestly, it started us down the road to our relationship breaking down entirely. It wasn’t the reason we are NC, but looking back, I can see her lack of interest in having me be part of a special moment in her life was symptomatic of some bigger issues in her life, which did eventually mean we no longer had a relationship.
How old are your children? Unless they have significant additional needs, I can’t imagine how they would impact on the ceremony, even as babies, if you aren’t performing it for others. If there’s interruptions, that’s not a big deal, you roll with it, it’s part of family life.
I mean, I think you should do what you want, it’s your wedding. But do consider how it might make your children feel if they are old enough to know they’ll be missing out. If it was me personally, I’d have a registry office wedding to include them and keep the logistics and legal aspects as simple as possible and then have a lovely honeymoon just the two of you.