DEET. It's just too strong for the children. So, last year I made my own repellent, and it worked very well. I've made it again this year, only with rubbing alcohol and a bit of water as a base instead of expensive vodka(fixative).
From last year's post:
"You can make your own with essential oils added to either oil, vinegar, witch hazel or vodka. To name a few, these essentials oil are known for their natural bug repelling properties: lavender, eucalyptus, citronella, lemon grass, lemon eucalyptus, peppermint, clove oil, rose geranium, cedar, neem oil, and tea tree oil." Read more here.
Update: I just harvested a huge bush of catnip, and I noticed here, it mentions that catnip is an effective mosquito repellent. I'll be trying this as well.