I am sure your dog and cat already have fleas on them unless you have them on a flea preventative. If not, they need to go on one immediately. There are safe preventatives to put on them. You could go with the type that you put on their backs, they have one that combines with the monthly heartworm pill, they have even come out with Comfortis for dogs now that is a pill. There is no excuse not to use it. If you neighbor boards dogs, she needs to insist that either they come on flea preventative or she will put it on and charge an additional fee of 20.00 for flea treatment. If she is reasonable about it customers would comply. I would never leave my dogs in a flea infested home. She is the problem, control her dog flea problem and yours will go away if you treat your animals too. Fleas prefer dogs and cats, I don't think they really care about chickens. They don't particularly like us either just will come for a munch when the canine isn't around.
Don't go crazy with too many chemicals on your lawn, it kills a lot more than just fleas.