With the best will in the world, sausage casserole home-cooked is not healthier than eating a healthy take-away, I should imagine the salt/fat levels are higher in the home-cooked food.
Ditto Gousto/Hello Fresh, one reason the Gousto food tastes so nice is it is full of salt and flavourings, lovely but not necessarily healthy.
I would carry on getting the take-aways or the healthier side of ready meals for a while yet, at least 3-4 times a week, with lots of fruit, bagged salad and pre-chopped veggies.
Then on the other days, give them fruit/snack on coming out of school, and once home, have pre-prepared carbs (rice bags, preprep mashed potato, baby potatoes, nice bread), protein (anything people like from sliced meat, preprep salmon, bean salad, different cheeses like goats cheese, feta salad) and some bagged salad/toms or steamed veg.
I think a lot of people assume cooking from scratch is always healthier, but this depends on whether you include a lot of cheap meats (nuggets, sausages) and add salt yourself. Some ready-meals aren't great, but Lidl do some really good high protein ones with complex carbs that are good.
I would not get up on Sat or Sun with a baby and two children and batch cook for any money. Your life is exhausting enough. I struggle as a lone parent to cook after a day doing the school runs/dealing with ill-health of kids, working f/t and getting in at 6 and being knackered. It's one of the worst bits of the day, so make it very very easy for yourself. Also, friends may help out -if anyone offers to 'help', ask them to cook something, I had a lot of support around meals in the early month or two of my husband dying and it helped a lot.