I agree on the phone front, great for little videos there and then and the 4K is not bad, plus the 240fps is a lot of fun for the kids. That did enjoy me chasing them round the house with a stabilisation rig for my Fuji but I'm hardly going to get that set up on the fly just in case. So for video the iPhone [In my case] rocks.
I'm happy with my existing set up for my family needs, usually just bring a couple [or three] lenses and a body [or two] in a small bag like the Ona Bowery. I can shoot away all day with that including their sports days, school plays, as well as just day to day happenings. I any of them want a more formal [LIghted] shot they'll just call over and sit in. I'm not about to go dragging a load of modifiers and stands and lights about at a family do unless that's expressly why I'm there.
I just like having a couple of primes and let the day unfold in front of the lens, more of the feeling of the moment when I do that but I know others prefer a different shot from time to time. Just getting out and shooting and never mind fretting over what gear you 'need' to bring with you would be a lovely feeling.