How to invite kids, but also give the option of leaving them home?

You don't have to word that, people know they aren't required to bring their kids. We invited lots of couples with kids and about 50% opted to not bring their kids. Especially the ones flying in from out of state. On our invites, we put "The Smith Family" then included the kids on the # we wrote on the RSVP card. We invited 30 kids total (under 21), and almost all of them were under 10. We included an insert card for parents with kids under 10, it stated what the kids meal was (chicken tenders, macaroni & cheese, fruit) and a blurb about the nanny service that would be available in the kids room. It was an insured & well-reviewed company that our venue often used. We linked their website in advance so parents could research if they wanted. The kids room was 100% optional, but our venue wasn't safe for kids to wander because it's an active equestrian center so there were animals & heavy machinery. Most of the parents with kids under 5 used the nanny service, especially during the ceremony.

We did this by inviting the kids, but having a late wedding. Our ceremony doesn't start until 5:30, so many of the parents (without promoting) left kids at home because they didn't want to deal with sleepy kids.

Technically Sunday, but of a holiday weekend. I have no issues with Sunday weddings, but if you are trying to go for an adult/party atmosphere I would have it on a Friday or Saturday.

Sounds like you and your fiancé want different weddings.

I had my wedding on a Sunday evening 6pm ceremony and reception followed at the same venue. Honestly, I didn't quite think too much about the time until I jumped on this site and saw all sorts of threads about timelines for Sundays and I kind of freaked out but honestly, it was amazing. All of my guests were on time and many of them, maybe 70% stayed until about 11:30 pm, with the wedding ending at midnight. We started by word of mouth talking to our invitees about how we wanted a kid free wedding and would be on a Sunday and quickly guests began making arrangements to have their children watched. I'd probably start at 5 instead of 6 or even 4 pm but either way it can def work!

Just because people are invited doesn't mean they have to come. I woudl imagine most parents of under 3 yo kids will leave them at home. Not all - but sounds like that's ok. Just invite them and let the parents decide.

I agree, you need to have a heart to heart about the vibe you want.

If you are really not for having kids (I kinda don't blame you) then maybe the reception is adults only? You could word that in the invitation. So if people really want to then they can come to the ceremony and brings kids and then go home with their kids or drop their kids off with a sitter or the venue nanny for the reception. I feel that is maybe a nicer way to kind of say kids not preferred but maybe I am wrong.