Lens Help...28mm or 24-120mm or 24-70 or even the 16-35mm??

I just made the jump to full frame (d600) and currently have a 50mm 1.8, 85mm 1.8 , and a 70-200mm f/4.

50mm isn't wide enough. I'm just an enthusiast looking for sharp images - shooting mostly family(kids), sports events with an occasional landscape (when I shot DX with a 17-55mm)

I know what I should do... which is cough up the $1600 for a used 24-70mm but I am trying to avoid spending that amount.

Im wondering if I could get by with just a 28mm 1.8 or spend a little more and get a 24-120mm (reviews on this lens are all over the place)?

or skip a mid-range zoom altogether and lean 50mm and go with a wide zoom like the 16-35mm f/4?