Sonos switching between internal system components on its own

What WiFi/LAN signal they’re connected to has little to do either with anything for now, as you’re using the line in function via the computer’s headphone jack.

I assume you’re using S1 to connect the controller to both the Amp (or is it really a CONNECT:AMP…is it white, or black?) and the CONNECT?

As a guess, you’re running into an ‘autoplay’ issue, where the line in on the other device is seeing a signal come in. You may want to turn off autoplay on both devices in the controller, and just use your selection.

You might also want to submit a system diagnostic within 10 minutes of experiencing this problem, and call Sonos Support to discuss it. Don’t post the resulting diagnostic number here. Unfortunately, neither you nor I have access to the hard data in it. 

There may be information included in the diagnostic that will help Sonos pinpoint the issue and help you find a solution.

When you speak directly to the Support staff, they have tools at their disposal that will allow them to give you advice specific to your network and Sonos system.

Your profile lists a Connect gen 1 that is S1 only and a Roam 2 that is S2 only, both can't connect to the same controller. The Amp can connect to one or the other, not both at the same time.

https://support.sonos.com/en-us/article/sonos-app-version-compatibility

Which controller(s) are you using?

Do you have two Sonos Systems (not Rooms) set up?

Which Sonos Rooms/devices are on which system?

Which devices are on which controller?

I'm not clear what you mean by "jump" what exactly is happening?

As others have indicated you need to advise us of the following:

1. Is the Amp the black or white in color. *
2. Is the Connect a Gen1 or Gen2

If you don’t know the generation of the Connect you can determine it by logging into your Account on-line at Sonos.com and selecting Profile icon > System 
 

 * If white follow the instructions above to determine the generation.

Thank you..!...I am beginning to conclude that my issues may arise from the attempt to integrate my connect gen 1 to my system due to incompatibility?

That’s is most definitely an issue. Let us know if you need further assistance.