We have eight children. Ages 12, 11, 9, 7, 6, 4, 2, 1. I become anemic after delivery, and take a about a month off (or at least with reduced schooling) when a baby is born, but the older children keep on with their independent work. When we’re back into schooling, we ease into it around baby for several weeks until nursing and napping are more predictable. When baby naps, we do some work together, and when baby gets up, it’s back to independent work, if necessary. I also use a sling to accomplish more with baby around. If academics seem overwhelming, it can also be a good time to focus on home skills – learning a bit more cooking, housekeeping, etc, since those have to be done anyways, and you will likely need the help.
Toddlers – ours generally haven’t been too much trouble. Most of the time I have success with rotating toys, letting them have scissors and paper at the table, or a tub of water with toys in the kitchen. I suppose it depends on how your house is set up also – we school in the dining room/living room, and the kitchen is open with the dining room. I have a playpen set up in the living room for a disruptive toddler, and they can always head to the crib/bed if they aren’t willing to play (reasonably) quietly or nicely.
It is also good to take short breaks with the toddler for reading times throughout the day. And have your older ones do the same, if possible.
I don’t have a lot of advice besides that. I would say that habit training is very important if you want to accomplish much with a big family. And it’s okay to focus on that for a while if you need to – it is part of crucial life skills and will ensure a smoother school day when you can return to a more academic focus.
Blessings to you and congratulations on the birth of your child!
Gaeleen