This is called an "L cut" or a "J cut" (and I show you how to do it in my book on Amazon, if you're interested).
The best way to do it is in Expert view. Put your main video (the one with the audio) on Video 1/Audio 1. Then add the cut-away video clips to Video 2, above the the main clip. Right-click on the clips on Video 2 and select Delete Audio so that only the Audio 1 audio is heard.
In short, yes that can done. In Premiere Elements, you can unlink video and audio and you can split/trim the portions of video and keep the portion of audio if you want to. Someone who knows basic video editing will be able to do these easily.
thanks so much for this! I am new to this forum thing and I wanted to mark both as correct but since the other post has a more detailed answer, I chose that one. Thanks again!
Thanks heaps! We will be purchasing shortly and are excited to start using it--sounds like it can do everything we need