Normally I'm in agreement with both yourself MM and Andrew(I@M).
But based on the OP's stated issue .. of using the 35/1.8 99% of the time and hating the need to back up more .. plus the rendering quality of a fast wide angle and fast aperture .. I'm not sure the 24mm at f/2.8 is as obvious choice as it may initially seem.
Remember, irrespective of format size, bokeh rendering is going to be the same for a given point of view .. with the smaller format you just see less of it in the final image.
Whereas, going to 24mm (to begin with) instantly changes the background blur, and being limited(relatively speaking) to f/2.8(where f/1.8 was previously an option!) .. final analysis is that the rendering won't quite be the same as previously.
If this member's predicament were mine, and funds were limited, my choice would be a cheapish newish Fx body and a 50/1.8, whilst still using the 35/1.8 Dx for now too.
side note: I've been thinking of acquiring a 35/1.8 Dx lens to use as a pseudo wide angle for a bit, to see if it's something I'd use .. for my D800!
If funds were available, personally, I'd be opting for a D750 + Tammy 24-70/2.8 VC for sure in this instance.
PS: the use of the term distortion, I actually meant perspective distortion, not barrel. Barrel can be 'fixed' in PP .. perspective is harder to do, if not impossible to do with respect to extension re-rendering.
PPS: You may notice over time that as your kids get older(and hence you do as well), that shooting from a distance in a more candid manner doesn't work. The kids seem to have eyes all round their heads, and notice any attempt to photograph them at any time. The problem with being at candid distances, is that they have a head start over you for when they run off into the bushes to get away from the crazy haired camera mad parent!
Staying closer therefore allows one to chain themselves to the children in question until the parent's need for more images has been satisfied!