Is it possible to prepare store bought corn tortillas so they don't fall apart?
It sounds like you're just buying poorly-made tortillas, or old ones. A reasonably fresh corn tortilla is plenty sturdy for use in tacos or enchiladas. As they get older, they dry out and become more brittle. If you live in a place with a large Mexican population, you may be able to find a local tortilleria which makes fresh tortillas. Failing that, corn tortillas from the grocery store can be adequate as long as they're relatively fresh.

You can also make tortillas at home pretty easily using just corn flour (also known as masa, masa harina, or maseca), water, and a rolling pin. If you want to shape them more perfectly, or if you're going to be using lots of tortillas, you can get a tortilla press:



They are usually made of iron or wood and will let you press balls of masa dough into perfectly-flat tortillas.