Hello and welcome!
Sounds to me that you've developed panic attacks. Everything you describe is pretty much textbook, from the irrational fears to the desire to avoid situations that cause you anxiety. You also describe a panic attack pretty much perfectly (which could be part of the breathing issue).
It's not at all abnormal that once a person has kids (especially someone like you who lived a kind of "on the edge" existence, feeling invicible), they begin to realize just how NOT invincible we are, and it scares the crap out of people. It's at that time, anxiety can be triggered, and for some people, they just cannot shake it off. Sounds like that's where you are.
It's normal to have certain fears, and worry about the safety of our kids, but when the fears become irrational, and when they become all consuming and affect our daily lives, it's time to get some help. You don't have to accept this as your new "normal".
You would start by asking your doc for a referral to a psychiatrist, who will thoroughly evaluate you and offer you an accurate diagnosis. There are many different kinds of anxiety disorders, if I was a betting woman, I'd bet you're dealing with panic disorder with a resulting agoraphobia (avoidant behavior of anxiety producing situations).
Understand this, this has nothing to do with being normal or rational, or crazy. MOST of us with anxiety disorders (I have PD myself) are completely rational, even analytical people, which makes it that much more frustrating and confusing. We torture ourselves because we KNOW our fears are irrational, yet feel powerless over them. That will change once you get some help. Therapy is a must. You will learn all about what's going on and different ways to cope and ways to stop that anxious reaction and "what if" thinking you're doing. It takes some time and some practice, but it's totally doable.
Also, medications are an option. Meds are not a cure, but they help to control the symptoms to get you feeling a little less anxious, so you can make progress with your therapy. Meds will help improve the quality of your life by decreasing the amount of panic attacks you have, and the severity of them. Once you learn how to dismiss the thoughts and take the control back, you'll be well on your way to managing this.
Don't get hung up on the "whys". It's virtually impossible to figure out why some of us end up with chronic anxiety issues...with the exception of someone with severe past trauma. There are theories that there is a large genetic component, along with other factors. This isn't a character flaw or anything of the sort. This doesn't define who YOU are as a person. All this means is you've developed anxiety that is affecting your daily life.
I agree that the neighbor situation is not good. Now, I don't believe that's causing these issues for you, it's just another thing that's triggering anxious feelings in you, and your history of living a more dangerous lifestyle in the past is feeding your fears. If at all possible, it would be great if you could start looking into changing your environment. Is moving a possibility?
So, start with your doc, ask for a referral, find out what you're dealing with and start discussing treatment options. There's nothing wrong with seeking help for this. Actually, it's the smart thing to do. It's nothing to feel funny about, or embarrassed about in any way. This is totally manageable. You're not crazy...but you do seem to be dealing with some sort of disorder...that needs sorted out. Just because you're a big "tough guy" doesn't mean you should somehow "man up" and just deal with it, or try to fix it alone. You'd be surprised at how many big tough men deal with anxiety disordfers.
Please keep in touch and let us know how you're doing. We have a great anxiety forum if you want to check it out. I think you'll be amazed at how much you'll relate to others there. Even just searching and reading will probably bring you to a lot of "a ha!" moments.
http://www.medhelp.org/forums/Anxiety/show/71
(Just a mini disclaimer..I'm obviously not a doctor and am not "diagnosing" you...but my reply is geared toward the assumption that you're dealing with an anxiety disorder....which is my hunch).