Sorry this is long, but I so remember this.
My mom was a single parent when she and my dad divorced. She had the same schedule as you.
She made us very organized. She did a load of laundry every day or every other day She popped it in the washer in the morning and then put it in the dryer when she got home. The dry clothes were always on one end of the TV room sofa. If you wanted to watch TV, you had to fold and then place the clothes in the correct places during commercials. Even your 3 year old can help separate clothing into colors. He can help fold small pieces of clothing and he can place the clothes in the correct rooms. If your son has a wagon he can pull them around the house. He can also take the clothes to the washing machine using the wagon.
When she made a meal, she made enough for 2 meals, so we ate leftovers every other day. We always had sandwich stuff in the fridge, so we could just have a sandwiches. New price specials come out on Wed, but the stores are packed. So went shopping on Thursdays we went straight to the grocery store for grocery shopping. We would get something to eat from the deli and then we would shop. This left less running around for the weekends. We would clean in the morning and then we could play at the park or go to free activities around town or play with our friends.
Sharing cooking with your mom is a great idea. In the beginning, you could purchase "mostly cooked" items like frozen lasagna that can be microwaved. Serve it with a salad and rolls. Bertolli pasta in the freezer is very tasty, look for coupons.
Also here on mamasource go the "Request" Page. On the left hand side there is a list of topics, push on "meals" and you will find a ton of previous requests for easy meals. Check out the responses. There are tons..
3 year olds love to be outside and running. Have "races" with him. Set up obstacle courses in the back yard. Do Simon says with lots of hopping, skipping, jumping. Let him be Simon sometimes get your mom out there to play too.
Find giant cardboard boxes and have him crawl through them. In the dark, give him a flashlight and let him crawl through them. Get liqueur sized boxes and tape them closed. Let him stack them like giant blocks.
We have a long driveway. I would park the car across the end of the driveway to block the street and use sidewalk chalk to mark off traffic lanes on the drive way. We would draw stop signs, cross walks, intersections and parking spaces. Then we would pull out every trike, wagon, hobby horses, skates whatever and have our daughter and neighborhood kids play "Traffic". If you have sidewalks, it would be awesome.
Make a deal with your son, that he can watch a video on Sunday morning if he will let you sleep late. Leave out some breakfast bars, fruit and a sippy cup of milk in the fridge where he can reach it to serve himself.
If your mom will watch your son one afternoon. Ask a single friend if you could go over to her house and take a nap every once in a while.