I’m not quite sure what you mean by “whatever selection I make on one I-Pad effects the app running on the second I-Pad” - if both iPads are looking at the same system, a change to what’s playing should be reflected in the other iPad. When you select a room and the music the associated speaker will play,  whichever iPad controller you use, the other should show that choice. Then, on either iPad, select a different room and choose the music to play there. 
You don’t set up one room with one iPad to control it, and another room with another iPad. A single iPad controller can see the whole system - all rooms and speakers. 

Swipe up on the Room bar showing at the bottom of the screen to see your other rooms/speakers. Selecting a different room here will then change the room selection and you can then select and play music to that specific room, independent of any other room already playing.

I’m having the same issue. Since the latest app update on apple we cannot play different music on each speaker. If we select a playlist for the kitchen that then changes to whatever playlist we select for our office or living room. It’s frustrating to say the least. We are both running the up to date apps on our iphones - it makes no difference at all by selecting the individual speakers. We’ve selected the kitchen speaker, started playing a playlist. Then go upstairs to the office, select a playlist which starts playing but that then overrides the playlist in the kitchen. Arghhhhhhhhhhhhhhhhhhhhhhh 

Do you use ‘Groups”?

Yes, but the speakers are not grouped when we try to play separate playlists on different speakers

It sounds like you aren’t switching rooms before choosing the other playlist.  Any music chosen is always going to play in the room at the bottom of the screen.  Before selecting your playlist, choose the room you want to play it in by swiping up on the room at the bottom of the screen and tapping on the room you wish to select.  Then start the playlist.  Repeat the room selection, then playlist start, for each separate room.  

I/we are switching rooms before selecting another playlist to play in another room. 

Do it again, then within a few minutes generate a diagnostics report and speak to Sonos support. They should be able to identify what’s happening. 
 

When you know, please post here so that we know what the solution is.