I'm not a child lover - i find it just as irritating when a child is allowed to run free, get under my feet, pick things up, cry uncontrollably and when parents don't have control on their kids. I know that's opening a whole other can of worms.
Haha a brave statement - wait for the backlash
I have two dogs, both of which are as you say chipped, insured etc etc. I also walk them on beaches and in areas with these leash signs and I dot walk them on the lead. I do try to avoid people as much as possible just in case you get some odd git who moans at you. This woman is a busybody and you get them - fact of life. Continue walking your dog as you do and let her rant and rave....loons everywhere