Heya,
I've done the whole 1D + big F1.4, F2 primes, zoom, etc, full frame with primes/zoom, etc. Unless you're just completely enamored with holding and looking at the gear more so than being in the moment with your family, it's all too bulky and gets in the way. And yes, 70mm is not wide enough all the time. Unless your goal is to only capture headshots with blurry backgrounds, candid portrait basically, you really don't need that big of a lens, nor the focal length, day to day with the family. Maybe more likely if you were doing sports with the family. But for the every day, at the house, out with the family, on a trip, etc, wider is going to do more. If your stuck on needing full frame, then I'd go for the 24-70 or even a 16-35. I stopped using my three full frames and my go-to for being with the family is a mirrorless APS-C with a pancake F2 lens that has a 35mm equivalent FOV and good TTL onboard flash, in a rangefinder style body (Fuji X100 series). I much more enjoy this. Just my preference. And that's from using 5D's and 1Ds full frames with 70-200, 35, 85 and 135L type stuff. I don't want all that bulk. Walking 20+ feet away to get a basic shot is just no fun and you're no longer with your family in the moment, you're on the sidelines just documenting everyone else's day. I like being able to hand my little camera around and someone else can take a photo too and I don't worry about it so I can have some photos of me too. And 9/10 in almost all situations with the family, I've never needed 200mm while actually being with them unless it was a sporting event or some outdoor thing. Heck, I spent a lot more time with a 17-40 with the family on full frame when we went out and on trips. I prefer wider with the family so I can get context of where we are and what we're doing. I don't want few blurry background headshots at some destination that no one can tell you're at unless you tell them, from looking at the photo.
So again, I'd favor a 16-35 or 24-70 / 24-105 on full frame for the "every day family" stuff. Even that is overkill. Get the 70-200 for outdoor & sports.
Making the equipment work for you instead of the other way around will kill the joy of it. And after the moment and time is gone, you cannot get it back. So my default response to anyone needing a "family" lens situation is to error on the wide side.
Very best,