Oh boy, I feel you on that. You are not overthinking at all. I know from previous experience when I was doing the pre-reqs, I've always had fallen back with keeping up my home and taking care of my family. I don't want this to be repeated. I am also going to start this fall, and before I even knew I was accepted in the program I have set up routines to make them a habit by the time I start school. I only have two kids, but they are much younger and very needy. As for my husband, he is not going to step up to help other than driving my oldest to school, soccer practice, etc. My youngest will stay at home with my p-i-l, but my m-i-l will only do the cooking, I do not expect she will clean the house or do the laundry (at her house she has a full time maid). Since I have started with the routines I saw that my house has stayed pretty clean and I only dedicated little time every day, but routines have to be consistent otherwise things will pile up very quickly and before you know it there will be more to do.
I have a morning routine of 15 minutes, in which I go through every bedroom make the bed and a quick pick up, then the bathrooms, where I do a quick wipe of counters, splatters on mirrors, swish and wipe the toilet. Usually it's not more than 5 minutes per bed/bath. I also make sure the dishwasher gets emptied in the morning, otherwise the sink gets full really quickly throughout the day.
In my evening routine I clean up after dinner and I set a load of laundry in the washer overnight, then I dry it in the morning. As your kids are older you can certainly give them specific assignments for after dinner. For example, one child clears the table, second child loads the dishwasher, third sweeps the kitchen floor, husband packs lunches and throws the trash, you can wipe the stove and kitchen counters, and your youngest child can put toys away or whatever your household needs are. Usually this array of chores is just mine and takes me about 20 min and I do it right after dinner. I think being specific about their chores is key.
As for keeping up the rest of my home I have set up a weekly schedule of only 10 min per day for that specific task. On Monday I change bed sheets and towels and I launder them. On Tuesday I purge mail and junk mail, boxes, etc, and empty all trash cans. On Wed I dust surfaces quickly with a Swiffer, I do not get into detail polishing my furniture. On Thu I vacuum and Fri I mop. I also do a load of laundry every day which I put in the washer in the evening right after dinner, dry it the next morning, then fold it and put it away before I go to bed. You can get your kids to help with that.
It probably sounds like I am going to clean all the time, but my goal is to maintain the house decent and livable, not shiny and sparkling.
As for meals I recommend you make a menu for 30 days with shopping list and all, and then repeat that every month for the remainder of the semester that way you will not stressed out when dinner time comes. If your family likes slow cooker food go ahead with that, it's going to save you a lot of time. Stock up on nonperishable as much as you can and household essentials because it will you save plenty of time later. You'd rather be home with the kids or studying than shopping for toilet paper.
I also recommend you get a planner and write down everything before hand: appointments, menu, chores that need to be done, your children's school stuff, etc. I started one like that and I was able to plan my meals, birthdays, chores, appointments, and everything in between up till December when the semester will be over. That way I don't have to think about all that stuff later when I'm busy with school.
I know I have blabbered a lot here, but I had same worries as you. I am glad you asked this question. I looked back at past experiences and I figured what I had to do in order to be better prepared. I don't want to neglect my family, but I also want to be invested in school because that's our future.
I'm sure you will be able to plan and prepare for what is soon to come. If you start now, by the time school begins both you and your family will transition very easy. Hope this helps. Good luck!