Antennas do not "create" harmonics or other spurious signals. But some
may be more "friendly" to radiating a second or third harmonic. Their
near field radiation pattern and coaxial decoupling contribute to the
near field strength of a signal. Due to the characteristics of some of
the most infamous antennas, they may radiate the same amount of R.F.
into nearby structures while running 4 watts, as another type of
antenna may do with 100 watts or more.

Bingo.

First, don't make noise. (clean rig)
Second, don't radiate noise. (resonant antenna)
Third, use an antenna pattern and feedline decoupling, so that the radiated
energy is up and away from the vulnerable system.

Distance, because of the inverse square law, is your friend. Double the
distance between the radiator and the target, and the signal drops to 1/4 of
what it was.

If raising or moving the antenna to a place where it couples
less RF into a home may just do the trick. Changing the antenna to a
better design may accomplish the same thing. Good RF grounding may
also minimize RFI. There is no "one size fits all" solution.

Another less often appreciated point, fixing any one thing may make an
improvement, but not solve the problem. Then the perception is that the fix
"didn't help" or "was worthless".
Old engineering maxim, if you can't measure it, you can't improve it,
certainly applies.

--
KC6ETE Dave's Engineering Page, www.dvanhorn.org
Microcontroller Consultant, specializing in Atmel AVR