I'm the "natural flea remedy lady" on this board.
Every summer when fleas are at their worst, I use beneficial nematodes (you get then at a natural or organic gardening store - and you can order them from natural gardening websites). These are microscopic organisms that you spray on your yard in the spring, after freeze danger. They live in the soil and eat flea eggs so that fleas cannot live in your yard - that is 9/10ths of the battle. If you live in a cold climate - you will have to reapply every spring - but here in Texas, I can go 2-3 years without reapplying. Another benefit is that the nematodes also eat fire ant eggs - so you won't have any fire ant beds in your yard either and that is important for those of us who live in the south.
Of course, fleas can come into your yard from other animals or the neighbor animals. What I do for that is to sprinkle diatamaceous earth (you can get it at a natural or organic gardening store) around the perimeter of the yard. It looks like powder and feels like powder but it is actually ground up sea shells and when fleas walk through it (from another yard to your yard) it cuts their legs and their body fluid runs out and they die. It won't hurt your babies at all if they step in it. I also sprinkle it on my roses when bugs start eating on them.
Anyway, beneficial nematodes will keep fleas out of your yard and diatamaceous earth will keep them from walking into your yard. Of course, it won't stop a flea from jumping onto your babies from another dog or animal. But this will just be one flea, an occasional one and you won't have the continual problem. Also, if you take the carpet out of your house, there will be few or no place for fleas to reproduce - and if they can't reproduce in the yard (the nematodes take care of that) and they can't reproduce in your house, then the flea problem is minimized without harmful chemicals on the yard or on your babies.
The only time I use Advantage or something like that is when we travel extensively. We have a doggie door and the boys go in and out all day. We have outside dogs on both sides of us and we never ever have flea problems since I have started using nematodes and diatamaceous earth (DE). Of course, you do have to reapply the DE after a big rain.