Aita to address invites to adults only, when i addressed a couple save the dates to the family (ie. The Smith family)?

It could create an inconvenience for those guests. Save the dates are supposed to give a heads up to guests about your date, and exactly who should save it. If you were going to invite children, but have now decided to have a child free wedding, I would just reach out to those individuals that will be affected and let them know that plans have changed and your wedding will now be an adult only fair, and apologize for the inconvenience. Since your wedding isn’t until September, the heads up will give them plenty of time to secure childcare.

It's not very considerate or polite to exclude people you indicated would be invited. I'd bite the bullet, personally.

Yes, and rescinding the invitation in part suggests you cannot afford the wedding anymore, even if it's not the case.

Yes as you already extended the invite. The time to decide if you wanted them there was before you sent anything to them.

You've given them the impression that it's OK to attend as a family. It's too late now to politely rescind that invitation.

What’s done is done and it’s impolite to revoke any invitations to kids at this point. It ceases to be a child free wedding when you invite infants, flower girls, ring bearers, etc and guests do get upset when they are told not to bring children and see others with them, though no one will say a word to you.

It is considered a bit impolite, but its also your day. If you want to be adult only I would reach out to those you addressed as a family and say that you understand addressing to "The Smith Family" implied the kids would be invited but unfortunately that isn't the case and that you just wanted to apologize and give them a heads up so when the formal invites come it isn't a surprise and to reach out to you if they had any questions.

Coming from someone who had a kid free wedding, it was so worth it!