The etiquette answer on this is clear – it is not rude to invite only adults to a party. There is no etiquette rule stating that children must be invited everywhere along with their parents. None. Significant Others have to be invited together socially, but not kids. So, from an etiquette perspective, your party is fine as you have planned it.
Stating “Adults only” on an invitation, however, is against standard etiquette. This is because it’s exclusionary. You put the names of the people who are invited on the invitation, you don’t include a list of people who aren’t invited.
These are the etiquette answers. Now lets deal a minute with the real world. Might some people think you are rude for excluding their Widdle Darlings? Yep, there are people who will think so. I wouldn’t sweat that too much. Them thinking you are rude doesn’t make you rude.
More seriously – might some people try to bring their kids anyway if you don’t make it very clear that they can’t? Unfortunately, yes. You know your guest list better than we do – are adult only parties completely unheard of in your circle? If so, you may very well run into problems.
I think the best thing is to make the invitations rather formal looking. Use white or ecru cardstock with black printing and formal, third person wording. Also use formal titles in the addressing. That is to say, “Mr. & Mrs. Whosie Whatsis” for married people. If you have any non-married couples coming, or couples with different last names, or whatever, and you need to know how to address them formally, let me know – I’m an event planner and I’m good with formal addressing. I could help you with wording the invitation, too. It needs to be formal enough that it will be clear that this isn’t some backyard BBQ that kids wouldn’t be noticed at.
On the RSVP card, instead of a blank line, use one that reads ‘number attending.’ Not ‘number of adults attending,’ because some might think this means that kids eat free or someething. Just ‘number attending.’ If anyone writes in more than 2, you’ll have to call them up and say, “I’m so sorry my invitation wasn’t clear enough. I’m afraid this is a formal, evening party and we can’t accomodate children there.”
Keep in mind, too, that you will have people who do not RSVP. Even if you include stamped RSVP cards. This is the number one rudeness I see from the guest’s side – failing to RSVP. You will have to call some people and see if they are planning to attend. When you call, say “I hadn’t heard back from you about my party on the 8th. I’m getting the numbers together for the caterer, so I thought I’d better call and ask if you were going to be able to attend. … Oh great! We were really hoping to see you there. So I can put you down for two, then? … Oh no – I’m sorry for the confusion. I’m afraid this is a formal, evening party and we can’t accomodate children there.”