Some cacti just grow that way. I think one of the most interesting things about cacti is the unusual shapes they develop. I have one that's fat, then gets skinny, then fattens out again. It looks rather like a small ball set on top of a larger ball.
You can remove the pups, if you like, and pot them up individually. Allow the broken/cut end to callus off before you put it on the soil to root.
I don't think the parent cactus will root if you lay it lengthwise on the ground. It might, I suppose, but I've not ever heard of that being done.
Repotting it into an azalea pan or some other kind of short, broad container should keep it from toppling over. Some pretty rocks in the container can help support the cactus, too.
If you like, you can just cut off the top portion to whatever length you want, callus the cut end, and root it as a new plant.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams