As for expanding the hole, I am still confident this post will answer your question.
Regarding the Schlage deadbolts, these are not great deadbolts. If you really want high security, you need to look at Mult-T-Lock or Medeco. These are far more secure for a number of reasons. First, they are made of much harder metals - if you feel them compared to another deadbolt there is a noticable weight difference. These deadbolts also often have balls at the end that push out of the bolt when fully expanded so it cannot be forced back in. Also, the keys for these locks can only be made (not copied) by the locksmith who originally created them (each locksmith is assigned a "keyway" and is the only locksmith who can produce the keys), this is handy if you have a cleaning lady or other service person since you can rest assure they cannot make a copy of the key for their friends. There are also metal rings you can put around a deadbolt that spin so that someone cannot use a wrench to twist if off.
If your doors hinges are on the outside then you can also look at having bolts installed on the inside of the door. This way, if the hinges are removed (pins popped out, or blown off with a shotgun), you cannot just pull the door off.
A heaver guage strike (the metal piece that goes on top of the hole where the deadbolt goes into) with longer screws will add extra strength to the deadbolt and hamper someone knocking down the door.
You can also place a cage in front of the door (which too has a deadbolt) but they are not attractive, and add an extra step to opening your door.
An alarm is useful but in a lot of cases, of someone knows what they want, they can be in and out before anyone responds.
A camera adds an extra layer of "don't mess with me" plus gives you a far better chance of identifying an intruder.
Making a wild assumption since we don't have enough information: I'm guessing that what you have is a grade-3 Schlage cylindrical privacy set of the sort that's available from every hardware store in the country. There are three pieces to this unit -- an outer knob with a hole in it, an inner knob with the thumbturn, and the latch mechanism.
The installation guides on the Schlage website are for one-side-keyed knobs, but the principle is the same -- in fact, the mechanism is close to being the same.
If you look at step 6 in that guide (sorry, I don't have that one image by itself), you will notice that on the inner knob with the turnpiece, they tell you to look into the knob and make sure the slot is horizontal. If you look closely, you'll also see that the flat piece which runs from knob to knob is horizontal.
That's what you got wrong. It is possible to assemble the lock with these pieces rotated 90 degrees -- but only if you rotate them in opposite directions, with the result that they're both at their limit and each keeps the other from operating. This also has the side effect of tying up the knobs in the locked position.
(This is a general hazard when assembling mechanisms that are only designed to operate through part of their rotation rather than being able to spin endlessly. The position of the parts in this cycle is known as their "timing". You got the timing wrong.)
Remove the knobs, and reinstall them with the flat bar horizontal and the thumbpiece turned to match it. That should cure the problem, unless you've managed to do something more weird than usual.
Best Answer
If you have an identical lockset, then you know exactly how many fastening screws there are. If removing them all doesn't loosen the cover plates, they must be held in place by adhesion to the door's finish.
Using your sharpest knife, carefully cut the paint or varnish adjacent to the cover plates. Score it all the way round, the gently work the knife point under the edge of the cover. Be very patient and pry only a little bit at a time.
You will improve with practice, so work on the inside cover plate first, leading to less damage around the outside cover to attract the attention of the HOA snoops.