I use no weed killers on my yard. Many are carcinogenic, and some though after dry are supposed to be safe are not what you would let an infant crawl in. When forced by fire ants or fleas I did do local treatments but fenced it off for weeks. Exposure to diazanon, malthion, and other pest products is just dangerous period. Weed killers and weed and feed I do not use, fertilizer I carefully screen, use organic, water in well, and keep dogs off for a long time. I pulled weeds and kept the grass well watered to combat weeds. I also resodded part of the yard when we moved for less cost than all that weed spray.
I no longer spray for roaches or bugs but do use boric acid which is safe enough to mammals to use as eye wash. It is quite toxic to bugs. Seal all points of entry into your home or have someone do it that knows how. The smallest holes are easy entries. I also do not use swiffer or floor cleaners which are pretty dangerous (vinegar & water only), glade or like plug ins, or let dogs near potpourri, or other cleansers. Brushing boric acid powder into your carpet if you have a flea issue keeps them at bay for over 10 years and is very safe. Google any of this stuff and research for yourself to be sure you agree before pursuing. Many of the poisons are also human neuro-toxic so be aware you can expose yourself and later develop neurologic illness and other issues 10-20 years down the road.
As for parks I usually avoided any area I suspected might be sprayed and stuck to the natural areas where I could help it. I also do not walk my dog in wet gutters where other people's yard poison can run off or allow them in other yards or runoff areas since you have no idea when they sprayed. Mostly school play grounds where young kids play, but off hours are much less poisoned than regular parks. I do wash my dogs feet esp with all the road salt up here and have a paw dip station since running water or a bucket is much better at removing things than a wipe with a wet towel.