Hi Melissa,
My recommendation is that you get a soil test done. You can usually have that done by mailing in a soil sample (mixed from about ten locations in your yard) to your state university extension office. That will tell you about the ph level in the lawn. Your issue might be a PH issue which can be fixed with lime or other soil amendments. You really need to get the PH right before you bother with anything else.
Your lawn looks nitrogen deficient. Clover is indicitive of that. However, as others have noted, clover can exist with your lawn. If I walk through the older, wealthier neighborhoods of New England (where I live) most of the lawns have clover in them. It was only in the 60s (I believe) that we started to try to get rid of clover. Clover actually improves the quality of your soil by adding nitrogen. So if you have it in your lawn, it is out-competing the grass.
If you don't want to use Ringers (which I don't because I have never found it near me), I would use "Milorganite" on your lawn. I can hear the collective gasp as I write that. Yes, it is made from sewer sludge (AKA fecal matter), but it is cheap, organic, and works well. It will also add some iron (greens up the lawn) and phosphorus (which promotes
root growth).
The weeds are another issue. I too have a wee one and don't like any chemicals on my lawn that are going to be tracked into the house. My recommendation is to pull them by hand. Yes, that is a lot of work, but that is how I do it.
The brown grass looks more like grass that just needs some
water to me. Thatch really exists below the top layer of grass. If you are really concerned, give it a like raking to pull out some thatch before you mow next time.