Instead of spraying your family down with the harmful chemical Deet, use Listerine. Pour the mouthwash in a spray bottle and spray the kiddies with it. You may want to use a nice, fresh scent like mint instead of the original Listerine. Also, do not use the whitening mouthwash; you risk staining or bleaching your clothes.
This will have to be reapplied more often than commercial bug repellants, but its safer for the family.