Cooking for kids
This pasta meal can be "decomposed" in its parts for picky eaters. You can serve the pasta and sauce separately, or serve kids the various components separately, raw or cooked. Just set them aside on a plate as you go.
If you want to use the slow cooker, you can try tossing everything in and setting on low for 8 hours. You will need to make sure that you have some liquid in there, whether it is 2-3 cups of vegetable broth or one or two 28-oz (796 mL) cans of diced tomatoes, some tomato juice, or a combination. Vary the amount of liquid based on the desired result (thinner or thicker sauce) but also depending on the types of vegetables used (mushrooms and zucchini will release lots of water while cooking). If you proceed that way, the result is probably going to be tasty, and more nutritious than anything you can buy ready-made, but a bit lacking in texture and aroma (partly because you are skipping the caramelizing and deglazing steps). If at all possible, do all the cooking on the stove top and then transfer to the slow cooker to simmer for 4-6 hours on low instead. That way, you will not necessarily save much time, but you can do the active cooking at the time of your choice and come home to a simmered dish.
Electric pressure cooker (Instant Pot)
Tomato-intensive dishes tend to not fare very well in the electric pressure cooker, so you would want to use no more than about 1 cup of chopped tomatoes here, and also add at least one full cup of water or vegetable broth. Make sure not to fill your pot past the halfway mark! Use the "sauté" mode on your machine and follow the recipes' steps up to #9. Then, lock the lid, flick the valve to "sealing", and set the timer on manual for 3 minutes. Allow the pressure to release naturally (15-20 minutes) and open carefully. Go back to the instructions from #10.