wow 40 is super cold in a home....seriously that is super cold for kids
I would invest maybe in electric blankets for the beds. Or get the electric mattress pads.....I am sure your beds are just "cold" to the touch and warmth right where ya need it, like the actual bed would be more important.
At least you can crawl into a warm bed and feel cozy and it would not suck out tons of electricity costs as trying to heat an uninsulated house with those windows.
warm the beds and at least the kids could sit on the bed and do homework, watch tv or whatever, but it would be a warm spot to hit when needed.
Heating a home where the "heat goes right thru the windows and the walls" is just insanity....I feel for you big time. It is throwing money right out the door and you don't even feel warm.
I hate kerosene heaters but they are good in emergencies when power went out for us in winter. But I replaced it with a propane fireplace which I love....and yes, the kerosene stinks!

and are dangerous for used as a primary source of heat....emergencies sure, heating a home permanently, I would be very very cautious on that one.
next crazy suggestion is MOVE. if at all possible I would move since you are renting. I know it might be impossible but keep an eye out for something to rent that does not require that all your money is spent trying to stay warm.......that landlord should be shot for renting that place to you in that condition....spending $1000 on heating is insanity and you must find a way to save money better than that in your daily life.
best of luck to you and I hope you can find an answer.....