The best thing to do right now is not do anything to the lawn. The lawn is going to sleep for the summer and doesn't want to be disturbed until early September. Just keep mowing it, but set your mower to 3" minimum.
You're definitely mowing too short. You
should be mowing it
down to 3", not mowing it down when it gets to 3". Being from central Indiana as well, I can attest that lawns around here love to be longer. Believe it or not, your lawn will actually grow in height slower if you do this, and you won't need to mow nearly so often, unless you want to. It also adds to your overall lawn health by allowing the grass to put its resources into plant health, instead of having to heal itself every time you mow. Instead of the grass putting all of its resources into regrowing the tops, it can build a healthy
root system. Set your mower to at least 3" and you'll see dramatic improvements in a few weeks, especially once the fall grass growing season kicks in. Its not the end all, cure all, but its your best bet right now. That should also help your thatch problem. The lawn grows slower, therefore creating less thatch buildup when you mow.
Stop watering over the summer. The grass is going dormant and doesn't benefit from watering. However, your weeds love the water! If you want weeds, then now is the time to water! So stop the watering. Your grass will get a little brown. That's what healthy grass does around here in the summer. The main thing is you won't be watering your weeds while your grass sleeps.
Aerating might be a good idea in your situation, but I would leave the thatch where it is and not overseed. You have grass already. It will spread itself via its rhizomes and runners. The thatch will get better as you do the things to repair your lawn. The aerating will help get water, oxygen and nutrients to the top layer of soil. Topdressing with a good homemade compost would be a good idea. If you do these two steps, wait until the beginning of September.
Talk to your hubby. He should realize that your lawn is a chemical junkie. Just like the human variety of chemical junkie, it will take some time to rehabilitate it. In the mean time, it can get a bit ugly. Again, this is just like the human variety. Don't panic. This is normal. It will get much better in time. And you'll have a beautiful lawn that your beloved child can safely play in. The key is patience.