Up sh*t creek...

Okay, I guess I need to make some clarifications. This is an old National Homes Corporation prefab house from the late 40s/early 50s. It is built on a slab, and is a single story. The direction the clean out plug in the floor drain points is 90 degrees away from the bathroom. The orientation of that picture is the clean out plug is to the west, the bathroom is to the north, and the kitchen is to the south. There is a small clean out/y-pipe to the southwest where the kitchen sink drains, and there is a larger clean out/y-pipe almost directly north where the bathroom sink drains. This larger y-connection is also at the base of the main vent that comes down from the roof. The toilet drain is under the floor, but I imagine it meets up with the main line down there somewhere. All of these connections, drains, y-pipes, and clean outs are within five feet of each other. It was my understanding that they all pretty much met in the vicinity of the floor drain, and then began their path toward the outside of the house. Not being able to see through concrete, my estimation in that regard may be a little faulty. I've included a rough, not-to-scale representation of our house. If you look in the laundry room, the red dot is the floor drain with the stuck clean out plug. The two blue squares are the y-pipe clean outs. The one behind the washer and drier is the larger one at the base of the vent stack. The one behind the sink is the smaller one. Is it possible to reach the main line if we were to snake either of the two y-pipe clean outs? I know I can get those open. Thanks again for all the advice. Even if it isn't something that we can feasibly do (i.e. costs money) it is still appreciated.