When your yard is in that shape, it is pretty difficult to get rid of those weeds. You can do it but it will take some work. I would urge you to not use chemicals such as Roundup - it goes into the watershed and is very toxic to birds, small animals and the like. Also, I would never use Roundup in an area where my Rexy and Rowdy would be walking - even weeks later. It is extremely toxic.
I don't know where you are in Texas or if you are able to consult an organic garden store, but if you can, they can help you. It will take some time to get control of the stickers, even if you use Roundup (and I hope you don't). The seeds for new plants are already in the ground from the stickers that have been shed off. You can start right now putting down corn gluten (get it at an organic garden store). It is a pre-emergent, meaning that you put it down and it prevents sticker seeds from emerging into new plants. I would advise you to get a device called a weed popper - it really pops up the weeds and they are then easily pulled out by hand. You will still need to use a pre-emergence (corn gluten) even if you pull up all the sticker plants and other weeds because they have already let off stickers (seeds).
The BEST way to have a weed free yard is to plant some sort of THICK grass - like St. Augustine - but I don't know how far north you live. If you live farther north than Austin, then it really gets too cold in the winter to use St. Augustine. If you get rid of the weeds and plant a thick grass, it will choke out the weeds on its own. I have St. Augustine and I have not used any weed killer in my yard in 20+ years. You fertilize in the fall and spring with a slow release organic fertilizer (that won't hurt your Yorkie kids). You spread some compost in the spring and aerate the yard if your soil is hard and compacted. Any organic garden store can tell you how to do all of this. It has been proven that using organic products on your yard will do much better than things like Scotts fertilizer and NEVER use a weed and feed in your yard, it will KILL your trees!!! The non-organic fertilizers actually deplete the soil of natural and beneficial components needed for a healthy soil and beautiful yard. The key to a great yard is a healthy soil.
Now for the fleas. Beneficial nematodes are the answer to flea control in your yard. Read more about them here
http://www.marchbiological.com/L/ben...nematodes.html They are microscopic organisms that feed on a variety of soil insects and they will keep fleas, termites, fire ants, etc. out of your yard.
Of course, that does not mean that your baby won't get a flea when they go on a walk or that a flea might crawl over into your yard from the neighbors yard. But that can be controlled by bathing your babies in Dawn dishwashing soap or some other non-toxic method.
The nematodes will also keep the fire ants out of your yard and that is a great benefit to those of us who live in the south. I have used the nematodes for 6-7 years and have not had a flea or fire ant problem in all that time. I have outdoor dogs living on both sides of my yard too. The nematodes work great!
You can usually get them at any organic gardening store. They can also be ordered, but they must be kept cool during shipping or they will die, so if you order them, be sure the supplier plans to cool ship them. Also, follow the directions EXACTLY for putting them on the yard. You will have to water your yard in the summer when it is very dry, enough so that the nematodes do not dry up and die - maybe once a week or so, if it is not raining.
Also, I put diatamaceous earth (DE) around the perimeter of my yard to keep the fleas from crawling into my yard. It works great, but it must be reapplied after a heavy rain. It is also a non-toxic pest control substance.
http://www.hydromall.com/happy_grower16.html I sprinkle it on my roses to control little pesky bugs who want to chew the leaves!!! You can also get DE at the organic garden store.
Your organic garden store personnel should become your new BEST friend!
Good luck!