How can I git rid of fleas effectively and safely around children?

the most effective treatment will be an aerosol floor treatment, not the "bomb"...the bomb uses an insecticide called pyrethrin..there is no residual to it so it will only kill what fleas they contact, so a few hours later when more fleas emerge from the pupa stage they will be unaffected. There are some foggers that do use a residual insecticide, but I wouldn't want to have it all over everything (the pyrethrin totally dissipates after a few hours). With the floor aerosol flea product you are applying to the floor itself, they will contain the insecticide for the adults and an IGR for the immature. To correct some mis information given, the eggs are not half the battle..they hatch into a maggot like larvae, not a biting flea. Any of the flea treatment products with the IGR will kill the eggs along with keeping the larvae from turning into the biting adult flea. It is the pupa stage that the flea emerges from and at times the flea numbers reappearing can look worse than the original infestation. If the fleas did come from the puppy, you do not to do anything to treat for fleas, for the most part people are too clean for an infestation to get started...if by chance you have stray animals living around the house or yard, that could be where the flea problem is coming from, but once again without an inside host, the fleas will not populate...if an animal has access under the house, that could be where the infestation is and some are finding their way inside.