...most of my shooting will be of my kids/family and will consist of indoor and outdoor shots equally.
I think I'm going to go with the 70-200 first and then probably pick up the 24-70 when it is more readily available.
I think that's a great choice!
Some examples from me...

EOS 5D Mark II, EF 70-200mm f/2.8
L IS II USM @ 70mm, 1/250 s, f/2.8, ISO 100

EOS 5D Mark II, EF 70-200mm f/2.8
L IS II USM @ 70mm, 1/640 s, f/2.8, ISO 100

EOS 1D X, EF 70-200mm f/2.8
L IS II USM @ 70mm, 1/200 s, f/2.8, ISO 100