How do i mitigate this?

I think unless the invite says please no kids people don't think about it. I'd just reach out and let them know its a no kid event. I honestly wouldn't think they'd be offended, I see way more weddings doing this nowadays.

“Sorry for the confusion but our wedding is adults only. We hope you’ll still be able to make it!”

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This is what I was typing so this lol

Sadly you need to say adults only otherwise people try stuff. I would message or call her and let her know that you noticed she put her child but that it is an adults only wedding. If she argues just explain that is why you put only her and her husband's name.

“We received your RSVP and we’re so glad that you’re able to attend our wedding. Unfortunately this is an adults only event and we won’t be able to accommodate the children. We hope you can still make it, but please let us know if this changes your RSVP.”

View Quoted Comment ^This is perfect!

View Quoted Comment I have invited older (7+ years old) kids and of course the ones that are in it and their siblings. Just really frustrated with it nonetheless.

View Quoted Comment I don’t think there’s any way to tell people that their kids aren’t invited but others are without being rude.