"Please leave me alone" is what I use when my glare of death fails and I do not care if it's children or not. If kids are going to do activities that adults also do then they have to be prepared to be dealt with the same way. Hustling strangers is still off-putting to many whether you are 6 or 60. If my distinct "leave me alone" look fails then the person is going to be told outright to leave me alone. It's not OK to hassle strangers for a buck whatever the cause. A table with a sign asking for donations at the mall is fine, approaching me and asking for cash is not OK with me. Sometimes it feels like many, many people in public spaces seem to feel that I exist solely to fund their monetary project du jour.
If I am followed, asked repeatedly for money after making a point with my body language of being uninterested then you are not going to get a "no thank you", you're going to be told to leave me alone. To me a "no thank you" is a response to a legitimate question or in a conversation I am choosing to have with someone. I do not view public begging as asking a legitimate question; at least from my perspective it is not.
I don't know what has changed but the only public begging that was around when I was young was the SA bell ringers. Public begging was something that happened very, very rarely and even then usually only is larger cities.. It's reached the point now, where it's just too much. Heck I can't even buy a hamburger a lot of the time without being hassled to "make a donation". Being hustled all the time by people who just have their hands out has caused me to severely restrict my charitable giving.
I absolutely ignore anyone soliciting, kids or not. I don't think it hurts for kids to come to understand that many people hate the behavior they are engaged in.