You have power at the switch, but not at the outlet that the switch is wired
to? Now you know perfectly well that is not possible unless there is a
break in the wire. Do you mean the GFCI has tripped, or there is actually
no voltage going to it?
Maybe you you can explain what your tester is, and how you are using it.
However, if you have two parallel GFCI outlets, and something is running in
one, if you jump H-N in the other, it could trip. The neutral is "hot" in
that it is returning current to the ground. Normally you would not notice,
but if you short H-N, some current will return via that connection since it
is as good as any other direct ground. Since there is an imbalance on the
H&N in that GFCI it will trip.

However... if your garbage disposal and dishwasher are normal build-in
appliances there is no need to use GFCI outlets with them.