Around here there is a "two heartbeat" rule for bedrooms (newborns are kind of ignored lol), but this only applies to rentals. Certainly double check the applicable state/county/city rules though... even if a LL is ok renting a unit out, you could find yourself being given notice if neighbors complained or if the LL changed.
Back to the original question... HS family of soon to be 6 here, living in a one bedroom cabin. We're building an addition which will include another bedroom as well as a living room (when we moved in as a family of 4 a few years ago the cabin was a single room with a sleep loft so having a "real" bedroom and "real" living room is wonderful!). Since we moved from a 4 bedroom, 1600 sq/ft house with a finished full basement and finished attic I had to get pretty crafty! LOL
Do you live near an IKEA? Even if you hate their stuff, it would be worth a visit to check out their sample rooms... I'm always impressed with how much they can fit in their sample rooms without making it feel crowded or cramped. The website has some stuff too, but actually being in one of the sample spaces and seeing how the pieces fit together might help you brainstorm solutions. And if you do happen to like the style then IKEA has gobs of space saving and organizing items (since European living spaces tend to be a lot smaller than North American norms IKEA has a lot of "small scale" furniture, or multi-use items).
The thing that saved me was remembering to build up... bookcases or book shelves or some other storage cube system stacked all the way to the ceiling can add a lot of storage to a space without using up a lot of floor space (if you're allowed to hang shelves, you may be limited to bookcases/cubes that can be tethered to the wall with minimal damage to plaster). Our living room has floor to ceiling bookcases on one wall (I use a ladder, and the top two shelves hold long term storage pantry staples), other sections of the house have floor to ceiling cabinets (bathroom style shallow cabinets from a salvage yard, stacked one on top of each other to create a wall of hidden storage) or shelves above windows and shaker style peg rails at about chest height. Actually, the shaker style is a great inspiration for compact living though to really "do" the style requires a much more minimal style than I have!
We use benches instead of chairs on two sides of our dinner table... the benches open and/or have shelves (the shelved ones were originally sold by IKEA as shoe benches for an entry way) and homeschooling stuff goes in the bench/on the bench shelf and work gets done either at the table or on the couch or on the kitchen floor or outside... oh and one wall I stacked bookcases floor to ceiling. Workboxes and things the kiddos need frequently goes on the lower shelves, other homeschool stuff goes higher up. If you wanted to put it in the kiddo's bedroom, maybe look into hanging shoe storage units (the kind with pouches) or IKEA hanging storage tubes or something similar... that way you could keep the "school stuff" contained and off the floor, with maybe a small table and storage bench so "school" could be hidden away. I really don't like using sleep spaces for stuff other than sleep though so "hiding" it may not be an issue for you/your kiddos.
One thought about a sofa bed or futon... having a small sleep loft for 5 people means that we lay out mattresses each night and put them away each morning. It's more work than it seems like it should be, but the loft is a wreck if the beds aren't put away each morning. Since it IS a loft and I CAN ignore it is necessary, it's not too bad. But I know that if I was using a sofa bed/futon in a primary living space I'd get frazzled pretty quickly. And given that my kiddos manage to get food/drink/small toys down into our sofa despite everything... I just know a hide-a-bed that they were using every day would eventually unfold to reveal a spilled drink or squished banana. And I'm positive it would happen at the end of "one of those days". LOL I'd probably loft a queen sized bed for DH and myself and put our office/work space under that loft, or build some sort of private bed "cube" using curtains or bookcases or room dividers to seperate it from the "public" living room if I had to go with a "living/bed" space.