I run into this a few times a year with my wife and four kids. The reality is most of us function and connect better when we maintain some kind of hard physical outlet so understandable that you want to prioritize this. As for me personally, hikes with the family don’t satisfy that element.
What’s worked:
1) Bank a decent block before you leave. Enter the trip already in a rest week mentally. You’ll stress less about fitness erosion and have more bandwidth for the family.
2) Every 2-3 days, get in one quality effort. Prioritize intensity over volume given the time constraints. The research backs this up: 2-3 sessions per week at maintained intensity preserves most aerobic fitness for 2-3 weeks even when volume drops 50-70%. For me this is a 45-60 min VO2 session — drop-in gym, hotel room on the trainer, local trail, rower, whatever’s available. I use a simple one-on/one-off structure so there’s no complexity, no equipment dependency, and it’s over fast. Communicate it in advance, fit it around the trip, and accept that occasionally it won’t happen.
Bonus if you can find a local hill or kom to attempt as that hits the fitness plus exploration aspect.
3) Shift your satisfaction metric. Over the years I’ve found I can get as much contentment out of a constrained workout executed under real-world conditions as a longer one done completely on my own terms. Ask me on a Monday morning if I had a good weekend after multiple birthdays, sports games, meltdowns and much of it depends on whether I shoe-horned in a couple workouts over the weekend 
It also models something worth showing your kids that family comes first but health/wellness/personal growth are major priorities, and that you can be flexible and adaptive without compromising it.
Good luck to us all!
