Checked baggage is definately not an option. Your luggage probably will fit into the room, although it might be a bit tight. Especially during the day, since you won't have much floor room. You might be better off leaving the duffel bad downstairs in the luggage rack.
And yes Superliner sleepers do have a luggage rack downstairs, just like the coaches. Putting a car seat in the standard room will be just about impossible, unless you keep it on a seat during the day and at the foot of the lower bed during the night.
I also don't know if the three of you are going to fit in the lower bed, it may be possible but it will be a tight squeeze. That may mean that you will have to put the kids in the lower bed and yourself in the upper bed. Under no circumstances should you put the 2-year-old in the upper bed. The safety straps will only keep an adult or a child that's at least 3 and a half feet tall from falling out.