If I remain at my original state university and become either a transient or non-degree seeking student at another state university, but don’t send my transcript, is there still a chance that I’ll get expelled from both schools?
When you apply to University2 as a non-degree or transient student, ask them specifically about the paperwork that they require. They may want your transcripts. They might not.
Talk with University1 as well to verify what the status of credits earned at University2 would be. Will they apply to your degree program? If they won’t, will they still need a copy of the transcript so that your records at University1 are fully complete?