As for what exactly goes wrong with DCF77, that is pretty obvious from the two spectrum-analyser traces provided by that signal: It gets overloaded with AM noise which the simple AM-discriminator receivers used in clocks cannot deal with.
You could improve the S/N ratio by:
- separating the wiring for the two systems as much as possible, and fitting a mains noise filter to keep the loop signal out of the mains wiring.
- putting a remote (ferrite rod) antenna on the DCF77 receiver and experimenting to find a quiet location (possibly the interference can be nulled out by rotating the antenna).
- attending to the shielding, earthing and balance of the lawnmower loop (especially shielding and twisting the feed wires).
You could document the problem and write to your local radio licensing people. Unfortunately, I expect that they would consider that neither the DCF77 clock or the Lawnmower Loop come under their jurisdiction.
You could also write to the manufacturer of the loop and ask for their assistance. They may be surprisingly helpful.
Finally (if you haven't already) you could research the methods that Radio Amateurs have developed for receiving VLF signals in noisy domestic environments.
Bottom line: In my experience, correctly earthing the loop and shielding the feed wires should do a lot to eliminate the interference.
But as before, you need to understand the modulation characteristics of the lawnmower loop in detail. What bandwidth does the system actually need to operate? Can the interference be reduced by fitting a better low-pass-filter to the loop transmitter? Can you put a notch filter at 77.5 KHz?
My point is that John F. Consumer will likely conclude that his "radio controlled clock" is dying, throw it out, waste money on another one, and maybe never make the connection to his (or his neighbors) lawnmower robot.
And more importantly, that if popular enough, such (badly designed) signals will eventually make VLF timekeeping useless for everybody.
Like any Broadcast service, VLF timekeeping relies on a saturation signal so it can override domestic electrical noise.
The level of Electrical Interference is steadily increasing world wide. Already services such as AM Broadcast Radio are unusable for many people.
The problem is caused by (1) the laws of physics, and (2) by our compromised EMC regulations.
At least your European EMC laws are much improved over the watered-down American ones.
Bottom line: The issue is much bigger than just VLF Time keeping.