Well, it's tough to know how close you came to getting the chop, without actually getting it. But...
Ascending the Athabasca Glacier on the way to the neve of the Columbia Icefields a serac (huge block of ice) about the size of an office building came off of Mt. Snowdome and obliterated our track - where we'd been just a couple minutes prior. We got peppered with debris, but otherwise, not a scratch. Percentage? Can't tell? Feeling? 200bpm heart rate.
On Mt. Andromeda, we had some surprises ascending the face, with ice where we'd hoped there'd be snow - oh well. Six hours of ice climbing instead of three hours of snow climbing. Then as we traversed the ridge to get to the descent route, our blue-bird day turned into a nasty white-out. We now had to grope our way along a ridge barely 40cm wide in many places. Hours of careful stepping finally got us to where we'd begin our rappels. But the storm had buried the bolts that we'd hoped to use - placed there by Parks for the safety of climbers. We dug bu couldn't find them. Finally, with hypothermia a reality, I placed two pitons in a crack. They could be lifted out with my fingers in the vertical plane, but seemed to hold well enough when loaded with a down-pull. No one wanted to go first. Luckily they held and we were able to get down. How close was that? Pretty close, but again, it's tough to know. During the 30 hours we were on the go that "day" there were plenty of opportunities for things to go sideways fast.
On a peak in northern Banff I was ice climbing over an overhanging bulge. I hate overhangs, with my asymmetrical arm strength, I usually leave leading those areas to my buds. Today, I'm on the sharp end of the rope and it's overhanging. For F-cks Sake. I think back to almost exactly a year prior, in the same place, where we didn't get past this point thanks to a the body of a falling climbing crashing past us as we rounded the shoulder to this spot. We rapped to where he'd landed expecting to find a body, but instead two multiple compound leg fractures and a while lot of minor injuries. The remainder of our day and a bunch of the night was spent in a rescue. Luckily today we're the only ones out. I've got a screw into the ice at the base of the bulge and I'm getting near the top. Hey! Feels good. I hang from my right ice tool and shake out my left arm. Suddenly I'm airborne. OH SH!T!!!! The rope catches the screw and the luckily the screw holds and then the rope stretches. SMASH. I crash into the ice with my side. I'm not only alive, I don't even seem too badly hurt. As I'm gathering myself and doing an inventory of bones, it's feeling very wet inside my right boot. My crampon front point impaled my calf when I hit, and now I'm bleeding. I still feel incredibly lucky, but the day is over.
The tough ones to assess are ski lines. It's impossible to know how close it was to an avalanche. I've skied those lines that are 35-40 degrees (prime avalanche angle is 38) and it's probably one of the riskier things we do based on stats. Many more skiers are killed than climbers.
So, it's tough to know just how close is close, but it's sure a lot more than some other things I do. I could type all day with not dissimilar examples. (electrical storms, crevasse falls, solo rock climbing, etc)
So, this is an interesting point...
You discuss mountaineering as though death is literally always hanging over your head. If this is not hyperbole, perhaps you should begin each excursion, if you do not already, by candidly saying to your wife and daughter "I might not be back but I am okay with that b/c my excursions rank in priority to being there for you".
I never leave thinking "well, this is it." But, the conversation you quote is probably there, just unspoken. It's a very, very difficult thing to describe. It's not that one thing is more important than another - it's that they all are. Time with my family is very important, but so is the time I spend climbing and skiing. I can't imagine not having either. My wife has a very difficult time understanding, my daughter less so as she feels a lot of the same pull that I do. But, maybe some clarity (or not!) will come if we go back over 30 years.
The first time my wife "met" me was a September day at our high school. I was riding an obnoxiously loud four cylinder performance bike and rode through the school parking lot and onto the sidewalk, down the path, and parked by the entrance to the school. While the boys in our school were jocks with buzz cuts, I had waist length hair and a scraggy beard. The previous year I'd been suspended 13 times for mostly fighting. I had a shady reputation and most it was well deserved. By the time we were married, she knew not only that I did dangerous things, she also knew it wasn't a "teenager phase" or something I'd "grow out of." It was interwoven into my being. She came to my races - motocross and superbike - and watched as I flirted with disaster. She watched me rag-doll down the track at 210 km/h and be taken off in an ambulance. She's nursed me though broken bones and dislocations and other injuries caused by motorcycles, cars, and climbing/skiing.
Many non-risk-taking spouses of risk takers have wondered what it is that makes them endure the sleepless nights and worry and potential loss of their loved one, and they don't seem to be able to come up with real reasons other than "he/she is just the one."
One of my biggest personal losses came quite some years ago, and his widow remarried an accountant, hoping to escape those worrisome days and nights. The guy was awesome - accepting of her children, super reliable, liked to BBQ for thrills, and doted on her. And she has since divorced him and hubby #3 is a climber.