oberkc

While this does not answer the question directly, there might be another option...
First, disable the notifications via the Ring app.
Second, create a notification in IoX, triggered by the Ring motion sensor.  (This notification could certainly be paused by whatever method you have in mind.)
Third, send this notification to your phone via UD Mobile.  (May require the notification plug-in in Polyglot.)
I do not recall a means to pause Ring notifications via ISY.  I believe the Ring app allows notifications to be set only to occur within a defined timeframe, but that is the extent of my recollection.

I have both running.  I don't remember any special tricks.

Have you disabled program A?

My whole experience with the IoP and PG3 has been odd (putting it kindly).  I had a working ISY-994>PG2.  I was preparing to migrate to IoP by updating the software of the IoP.  The results included breaking my ISY-994>PG2 relationship.
 
I thought I had, but I can see it was not obvious, or perhaps answering the wrong question.  I have checked multiple times and my settings are correct as best I can tell.  Both show "connected".
 
I was on 3.1.8, but am now on 3.1.10.  It took me a few minutes to recognize that the update reset the username and password to default.  This did seem to have an affect.  Hue node servers are now showing connected on ISY-994 and IoP.  I tried installing the Hue Emulator node server on IoP and ISY-994.  No more errors and both are showing "connected".  I am going to call this a small victory.  The hue nodes now show up in "my lighting" , as does the hue emulator.  I will call it a big victory when I can confirm or configure all the programs and scenes with the hue lights.
 
Usernames are correct as best I can tell.  Both have been showing, and continue to show connected.  Both had some node servers working but others not.  But...the point may now be moot given that moving from PG3 v3.1.8 to 3.1.10 may have fixed the problem.  I will know more soon, but it all seems to be coming together now
 
The non-standard port was driven many years ago.  I had another device that also used port 80, so when I tried to access the ISY on port 80 from a remote location, it found the other device.  I gave the ISY it's own port at that time and things have been working well, so I never changed it back.
I will continue to check out everything to see if it is working or, if not, update all the programs and scenes to their original configuration.

A scene relationship will not work for this case.  I believe a program is the solution you will need for this.  Assuming that you also want the opposite (button off when sensor on), such a program could look something like:
if
sensor is on
then
turn off button scene*
else
turn on button scene*
 
*Most keypad buttons cannot be directly turned on or off.  Most likely you will need to put the button into a scene and have the program control the scene.

One can set up an ISY program as a device for Alexa to turn on or off.  When doing so, commanding Alexa to turn off the device (the program, in this case) the program will execute the "ELSE" path of the program.  When commanding Alexa to turn on the device, the program will execute the "THEN" path.  Given this, my initial reaction would be to create three programs.  Logically, they could look something like:
Program 1 (the program Alexa would turn on and off):
if
nothing
then
run program 2 (if path)
else 
run program 3 (if path)
Program 2:
if 
from sunset to sunrise
then
turn on inside lights
turn on outside lights
else
turn on inside lights
Program 3
if 
from sunset to sunrise
turn off inside lights
else
turn off inside lights
turn off outside lights