You said you made a batch without oil and salt, and it tore very easily? That would be because salt is essential
, the problem is not with the oil. Salt strengthens the gluten, keeping it from tearing. I put as much as 2.8% (baker's percent) salt in my dough.
Oh, and to keep your dough from burning at the bottom, increase the hydration. Often I use caputo flour, but when i use an AP (Five Roses AP from safeway), I go to about 72% hydration. Makes it a little trickier to handle, especially with very little bench flour, but well worth it. You will get better oven spring, better charring and blistering, and a more delicate neapolitan-like crust. I think you will be pleased.
One more tip, if you aren't using a sourdough starter, give that a try; it makes your dough more burn-resistant.
About buying the pizza oven . . . just tell your wife that it's just as good an investment as buying a brand-new china set or 300-thread-count egyptian cotton bead-spreads, except that it's actually USEFUL. I kids. Be careful, "hell hath no fury . . . "