It sounds like you might have a sleep disorder commonly known as night terror.
https://en.wikipedia.org/wiki/Night_terror
While night terror is often accompanied by bad dreams that seem to be the cause of the flailing and wakening with panic symptoms, sometimes the sufferer doesn't remember any dreams and just gets the physical symptoms, which may be a response to stress, but may also be physiological.
In fact, awakening shortly after falling asleep is a symptom of some of the other types of sleep disorders that can befall people any time from childhood to old age (actually there are more than 100 types). Unfortunately, there is no simple cure to many sleep disorders, night terror (and delayed sleep phase syndrome — what I've had all my life) being just two of the common ones.
Most general practitioners don't have much education about sleep disorders and their solution is often just to drug the patient so sleep is deeper. This is NOT a good solution because it can cause other serious problems. If you can't see a certified sleep specialist, often neurologists or psychiatrists are able to diagnose sleep problems.
No matter who you choose, make sure they have access to an actual sleep clinic. I've logged a lot of time in a sleep clinic (participating in research projects even long after I was diagnosed). It's sort of like checking into a clean but minimalist motel. You show up with your suitcase and get ready to go to bed. Before you do, a technician will glue electrodes to various points on your head. The wires attached to the electrodes are plugged into a console beside your bed. While you are sleeping, the tech(s) is monitoring all the different people in the different rooms on a computer. If you can't sleep that's OK, but you just have to lie there. The tech can see what phase of sleep you're in, when your sleep in disturbed, when you're dreaming, when you're awakening, etc.
If you don't awaken yourself fairly early in the AM, a tech will wake you up when they need to do their shift change. They'll remove the electrodes and glue stuff before they send you home or off to work. It doesn't hurt a bit and finding out what's really wrong with you can be comforting and helpful. Depending on what's wrong, they might want to monitor you for more than one night.
If you live near a university teaching hospital or a regional psychiatric clinic, they usually have sleep clinics in their hospitals. I agreed to participate in a long study that was collecting data about the correlation of sleep disturbances to clinical depression, so I got my treatment for free from a very respected clinic, Western Psychiatric Institute and Clinic in Pittsburgh. Yale and Cal Berkeley were two of the other clinics that provided data to that particular years-long study. You don't have to do that, of course, but if your insurance won't cover your treatment, it might be an option to join a study group.
Other clinics are run by private doctors. Here is a website that might help you find a certified sleep specialist.
Find an AASM-Accredited Sleep Facility - Sleep Education
Best of luck. I'm sure your problem seems baffling and is disturbing to both you and your wife; the best response is to get a professional diagnosis.