I recommend spending your time making your home easier to clean....this has made a big difference at our house. First, I went through every inch of our home, not cleaning but just purging. We got rid of probably 1/2 of our stuff. Less stuff automatically means less to maintain, less that can be left out, less to pick up. Having empty space around is so calming for me. I feel like I do a pretty good job around here of getting rid of stuff, but it is crazy how quickly it can add up. We can survive with so much less than we have. After the purging I made sure everything has a place so it can be put away. When someone picks it up they know exactly where it goes.
Do you have a Mama friend who you can help with the purging to get you on track? It is so much quicker with 2 bodies to purge. Plus, having someone else to help keep you on track. A friend and I sometimes help each other out with big projects. One day she'll come to my house and we'll tackle something that has been bugging me. The next week I'll go to her house and we'll do her project. It is so much easier and really fun that way.
Getting rid of what I call "clutter zones". Having a chair in our bedroom just gave us a place to put clothes instead of putting them away. I hung a set of hooks behind our door where I can hang something I will wear again soon. It is a quick place to put it and keeps it off the floor and the bed. Less dishes means you will have to keep up with them and they won't get out of control. It sounds like you have a lot on your plate right now with work and your child. Give yourself a break. Maybe on the weekends (or busy nights) you pull out the paper plates and have a little vacation from dishes... we have a yard waste bin that we can compost paper plates in.
Also, starting little habits, routines can help. We spend a few minutes after dinner as a family tidying up. The kids each have to put away 10 things in the living room, playroom and their bedrooms. It doesn't keep the house perfect, but it does help. Every morning while my tea is heating up I get my hands on 20 things in our kitchen and get them put away. It doesn't keep the kitchen perfect but it does help. Just little pockets of time, a minute or so to put a few things away can make a big difference. It takes a while for a new habit to stick so go easy on yourself. After one habit (like a quick after dinner tidy) is set then you can add another one.
Sending you a big hug Mama! We can't do it all, none of us can. You are doing the best you can right now. If you can make your home easier to clean it will mean that cleaning is less of a job. I hope this helps.