Hello CaminoKlng71,
sorry to hear that. I was in the same situation as you, in my house they broke in now 3 times. First you will be fed up but then you will get mean.
To your first question, this is probably the most difficult one, i had the same problem, hysteric wife which is guided by emotions but not by rational thoughts. You have to show her that you understand her and you will put an alarm system to your appartment/house. Take the cheapest one from ebay you can find for about 50 dollars and dont tell her the price. Install everything and tell her that you installed an alarm system and that she can come back and look at it. In most cases this helps and you have your wife back and this will be worth the dollars.
To your second question: forget the alarm system you bought, therefore it had to be the cheapest one, this was only to get your wife back.
Alarm systems can be useful but a burglar who is not completely stupid will inform himself about alarm systems, too. The www is full of information about "bypassing an alarm system".
If you want to secure your property you do not have to think like a home owner, you have to think like a burglar, so read everything on the www about bypassing alarm systems and you will see why the dollars you spent are useless. Everything which works with current can be bypassed. Then these guys probably have other information about this theme which you can not find in the www. If someone comes out of jail, he is a perfect criminal because he learned all tricks there.
Most of the burglars are stupid and dont know what an electro pick is etc but it can be that the next time you have to deal with a clever one who will bypass every lock or every alarm system which works with current. So keep it very concealed and simple, with trip wires attached to something, just be creative and very mean. Depends on what you connect for exemple the tripwire this will either kill the burglar instantaneously or only warn you or the neighbours. Think in this direction. But there is again one problem: how do you explain it to your wife.
To your third question: Again you have to think like a burglar and not like a home owner. The more very visual signs you attach to your property, the more these individuals know that you are very vulnerable because you dont seem to have an other clue how to protect your property and this even attracts them.
All in all i would recommend you to use unconventional methods like tripwires attached to..... and such things. Things which a burglar isnt prepared for. The biggest problem will be how you explain this to your wife, there i cant give you any useful information, good luck