i'm a life-long mosquito bite sufferer and have had similar experiences to Nancy below. I've tried nearly every product out there, tons of repellents, skin so soft, B vitamins, garlic, the works- nothing stops them. i think if i poured citronella on myself and lit it on fire i'd probably still get bit. the ONLY thing that works is possibly toxic, but i do use it: DEET. i am going to try planting more basil by our kitchen doors tho- if it helps keep them out of the house that would be great, and if not, i love fresh basil :)
when i was a kid i was out on the back porch with my family (parents, sister, grandparents, aunts) for only a few minutes. after slapping myself repeatedly, i went back inside. i had 28 bug bites!! and noone else had more than two, most had none. also, my bites often swell up to a half dollar size and itch badly. when they love ya, they love ya.
here is what i do- avoid dusk/shady areas when possible, as well try to stay away from moist areas they like. my primary defense is to layer up w/ clothes (not fun if it's hot out). The mosquito repellent clothes seem to help a little altho you have to limit washing them. stay where you or other people can see your exposed skin so you can slap any that land for dinner. depending how bad they are, i spray DEET on the outer layer of clothes (prior to putting it on). i usually put more around the shoulder area b/c they are attacted to your head/face area. i keep a hoodie zip up sweatshirt around to reuse for this- it's thick enough to help keep from biting thru and to keep the DEET away from your skin, and you don't have to put a DEET covered product over your head. it's harder with a young kid tho, esp if they want to play.
for after bites, i use either topical Benadryl (gel better than cream, you don't want to rub it) or Stingease right away. taking benadryl or zyrtec orally can both also help. one last thing, it's only temporary but putting ice on them actually helps a lot while you do it.
good luck for your daughter, it's really hard to be the kid getting bit up, especially if you are active and want to play!
a while ago, i read two scientific articles about why some of us are preferred (i can't find the links to them) but the link below provides a simplistic version:
http://www.wisegeek.com/why-do-mosquitos-bite-some-people.... they also recommend a cedar oil product- it's a brand i haven't tried tho. (hey, something new to try! ;) )
the theory was that the way your body processes has a smell that is on your skin. by this theory, being freshly washed, not sweating, and wearing masking fragrances would reduce your appeal.
once again, good luck!