.....looking around for my sense of diplomacy.....not finding it.....your wife is [mistaken].
I don't know who told her it's not wise to carry with a round in the chamber, but they are wrong.
With very few exceptions, automatics are designed to be carried with a round chambered. Certainly all MODERN autos. If you have some kind of striker-fired auto, like a Glock, XD. M&P, etc, it is absolutely safe to carry chambered and was intended for this. And yes, even out 'ancient' 1911, about to celebrate its 100th birthday, is safe to carry with a round chambered, the hammer cocked, and the safety on.
Remember, that if you ever actually have to use this gun, your world is falling apart quickly. Your normal plans have all failed. All of the things you HOPED would keep you out of trouble DIDN'T. This means, you have to PLAN on EVERYTHING going wrong. You can no longer ASSUME that you will be able to draw the gun and rack the slide. Why? Who knows. You might already be wounded and not have the use of your other hand. You might be using your other hand to push back an attacker, DRIVE, or it might be restrained by an attacker. These are the kinds of things you will be dealing with when you are in a situation SO BAD that you have to fight for your life.
The alternative is what some call 'Israeli carry'. The idea is that you carry with a magazine in the weapon, no round chambered, safety off, hammer cocked. When you are ready to shoot, you draw with your right hand, and in the same motion, you rack the slide. A few weeks ago we had a guy in here arguing every reason he could imagine that this was the way to go, despite being shown the contrary. No matter how fast you are, no matter how much you practice it, you don't know that you will have two hands when you need to draw.
You need to learn a lot of things. How to clear a stoppage. How to reload quickly. How to do it with ONE HAND. Then how to do it with only your WEAK hand. These things are not optional. They are critical.
I don't know the size of the magazine you are carrying, but you also will be carrying one round less than you could. I don't base my plans on specific capacity, but it could make a difference one day.
Both you and your wife need a lot of training. Why her? The same reason you need a round chambered. You DON'T KNOW what the circumstances will be. You might be wounded, and SHE will have to fight for both of you. I am going to recommend getting some good training. something like the basic pistol course at Thunder Ranch. You might not be in a position where you can take a week off and drop about $2k to fly to Oregon for a pistol course, RIGHT NOW, but I will ask you to consider, how important is this, REALLY? If you are willing to be armed to protect your life, it is serious enough that you should get some training. Read every book by Massad F. Ayoob, but start with "In the Gravest Extreme". BOTH OF YOU. She needs to understand that this is a team effort. This is not something you can do once and say you're ready. Carrying a gun means you must commit to a lifestyle change, and an ongoing attitute of awareness and training. It's NEVER over.
For open carrying, I let the circumstances decide. If I'm out in the desert riding an ATV, yes. If I'm in downtown Salt Lake, no.