It sounds like you really want a no-kids reception, but you are worried about offending your flowergirl and her mother if you don’t invite the flowergirl. I think your underlying instinct is right; it would be rude not to invite her. Here’s why I think it’s necessary to invite wedding party children to the reception:
You don’t invite the children in your wedding party to the reception because it’s going to be fun for them or for you (as LucyLouToo pointed out, she was much happier as a flowergirl when she was watching Disney movies or had other alternate activities to distract her). You do it because of what it symbolizes: You asked your wedding party, including the children, to stand up with you as you exchange your vows on one of the most important days of your life, so they should all be welcome to share a meal with you at the reception. To ask otherwise implies that their value to you is conditional (which of course it’s not, but that’s the message it sends).
Additionally, inviting the wedding-party children to the reception is not so much for the children’s benefit as it is for their parents’. They are the ones receiving that message I talked about above. They have bought new clothes and coached their children to be part of this day, and as a gesture of your gratitude you should invite them to the party.
What I would suggest is to invite them to the reception, and then explain to their parents that since the kids will probably be bored silly at the reception anyways, you’ve arranged for a babysitter starting after dinner (MrsCPT had good advice about this), at which point the flowergirl can change into her special pajamas and the all-adults party can commence.
As others have noted, either the parents will be grateful and take you up on the babysitting offer, or they will go home early with their children. At that point you can’t control which and shouldn’t worry about which avenue they take. In the end this will be no different than what would have happened with the flowergirl and her parents anyway—either they would have hired a sitter for her and come to the reception, or they would have stayed home.
Furthermore, if you’re already inviting the ringbearer, one more child won’t really matter. It’s fairly common for brides to make an exception to the "no children" rule for the flowergirl and ringbearer, so I don’t think allowing the flowergirl too, even though she is local, would open the floodgates to inviting all the children.
The advantage of this arrangement is that you will be a gracious hostess, the parents can show off their children to other adults at the wedding during dinner, and afterwards you get a no-kids party. Everybody wins. Good luck!