If you can control access to the lawn with a fence (cutting out all but squirrels, etc), then going organic works well.
Core areate the lawn now and in earliest September (preferably after a rain when ground is soft; otherwise, water; rent a BLUEBIRD #530 from Home Depot, work over lawn from at least two directions); use items such as beneficial nematodes, molasses, and a fertilizer such as GREENSENSE 6-2-4. Have a look at Howard Garrett's website, www.dirtdoctor.com,
and his books. While not perfect, he's a great source as is the site. Stick with it, will take a couple of years.
I like to aerate and topdress with finely-ground compost, and heavily compost and mulch all beds. Get a soil sample from worst three areas and send it in for an analysis, and then use organic supplements to help correct defiencencies.
I've spread as much as one ton of supplements, and 8-9 cubic yards on a 5,000 s/f lawn (after double-digging beds) the first year, and had -- by far -- the most attractive yard on the block the next year. I generally dig the lawn its perimeter, add a little compost and a heavy cover of mulch to establish a "firebreak" from neighbors, from trees, and all other structures.
I also use a backpack sprayer to keep growth steady and lush.
And I use less water than those around me by year two, without having made the switch to xeriscape. From a neglcted, hard-as-concrete weed-filled former rent house (where water ran off in the street and there was more Dallis grass than lawn), in one year of steady work did 80% of the recovery, and by year two was more bug free than ever it had been before.
An organic program will bring a better variety of insects, etc, that keep problems like fire ants and fleas down. By the second year you will likely start to see more birds, different birds, toads, etc. Bug problems go way down (june bugs about disappear, as do roaches). Ton's more earthworms.
Trying to sterilize -- whether herbicides or pesticides -- is a disaster. Mowing too short is a bad idea as well. With either Bermuda or St Augustine, 2-3" at summer peak is good, gets those roots spread out and deepened. I mow twice weekly to keep growth spreading out, and clippings to a minimum during spring & early summer.
Just work with the dogs as to "landscaping".
Keep beds cleaned out (into a compost pile if you like), and use mower 1-3 times monthly even in Nov, Dec, Jan, Feb, March to keep leaves and other litter from accumulating.
Frontline/Revolution medication is a given, but the animal needs to be healthy. Healthy meaning truly clean water and best quality food, not just apparent absence of illness. If the immune system is built up, then fleas aren't quite the problem as before. The usual grocery-store food is generally lousy. You can try MUENSTER brand as a start, price is quite reasonable.
Inside the house, get everything
off of the floor that isn't furniture, and vacuum every inch of every floor every week, including closets
. If this necessitates a re-organization, then so much the better.
I know that South Texas is really badly off from the drought, and this can intensify the flea problems.
Have a look, too, at DVM Shawn Messonier's columns in the Dallas Morning News website on natural pet care.
Obviously, the public library on alternative pet care.