How must I treat my neighbor if she scolds my children?

Assess the issue. Be aware that your kids are learning every encounter and must learn to deal with other adults. Ask the neighbor for a review of the incident, ask the kids if appropriate. If the scolding is justified, reinforce it, even if you feel it a bit harsh and talk with the kids later. You do not want to create unruly kids that hide behind you when they break common rules of behavior.
Scolding neighbor. Tell her to please tell you first and that you are the parent. She really has no right to scold anyone other than her own children - unless they were engaging in some activity that might be dangerous.