The Canon gear would have to go, the age of my 7D is against it, time has moved on and there's much better options for £££ out there. I have 3 children, 6m, 2 & 4 so we're fully loaded wherever we go before I even think about camera gear. With all I've brought away, my phone has probably taken the most shots. I'll have to do some research on the Fuji 100-400, and the 1.4tc, if that's favourable, that'll be the direction I'll go in. Right now I'm favouring the XT-1 with the 23/56 and then either the Fuji 14mm, the Fuji 10-24mm or the Samyang 12mm. If anyone can chip in with their findings on any of these that'll be helpful.
I'm busy with a 10, 8 and 4yrs old so I can relate.........
With your current Canon gear you'd be getting a big jump in IQ just by purchasing a 7dmk2 or 80D compared to your 7d. I've found the 80D to be just a tad bigger than a panasonic GH3/GH4 micro 4/3 camera. 80D dual pixel AF technology with touchscreen is an incredible camera that can be used like a camcorder. Something you should consider if your doing video documentation of growing kids. If you like the 56mm range (FOV) you can lug a Canon 35 f/2IS and be incredibly pleased with the incredible optics of that small light lens for portrait type photos or when you want that 50mm kinda look.
My Fuji 16mm and 10-24mm is what I use to capture my style of photography for human subjects. The 56mm gets used more now too but up close photos UWA and wide angle is what I use to document. Hard to be physically far from my kids when they were young if your solo on an outing.
With my spider holster with thinktank lens bags and speed changer pouch I can lug a 2 lenses, camera mounted with lens (3 lens in total) and a fuji flash with no backpacks. I take my 3 children out solo all of the time even when they were younger. Just think I used to do this with my Canon gear!!!
Pick the tools for your application. I will either use two canon bodies at once or a combo Canon/fuji. Do what gets the job done
Now with my 80D, 5dmk4, and X-t2 I incorporate more video documenting my children's growth. I'm not a super skilled videographer so I actually appreciate my Canon Dual pixel AF more than my Fuji when it comes to video.