If the house keeps moving, repairing the cracks is near futile; they will return just about no matter what you do.
To repair them you'll want to add screws up each side of the crack (about 1" away from it)where you can get ahold of framing, then V-cut the crack itself to open it up a little and get more surface to bond to. Also important is to clean off ALL the previous patchwork, and the paint in the area you want to bond by sanding or scraping. When you re-mud, don't squeeze all the mud out from under the tape trying to keep the repair super-thin; this is where many people have problems. You have to leave some mud under the tape to get a bond, and "float" mud farther out on the wall from the tape to soften the thickness change. I'll often use a 12" taping knife to get a final on a repair of this kind.
This will give you the best chance of getting the repair to hold as any.