Overwriting a segment

It's doing that because that's what a punch-in is... it's designed not to get anything previously existing in the recording out of sync, and just insert a segment that you can define. This is pretty much the way all professional software does it.

Audition doesn't actually do what you want it to - I don't think that any professional software does (although don't quote me on that), so if you want to continue to use Audition, you'll have to change your recording method a bit. Actually the change will make the whole thing more flexible - what you need to do is record individual segments in Multitrack mode. If you record-enable a track, you can hit the Record button on the transport, and when you've got to the end of a segment, you hit the spacebar and it will stop. If you now move the cursor on a bit and hit Record again, it will create a new segment. If you look in the Files tab, you'll see them all as separate small files. Now, if your wife comes and does the same thing on the next track down, you'll have two sets of files, but you'll be able to pick them up and slide them about until you have the result exactly the way you want it. If anybody makes a mistake, you can just ditch that small file and record another one. Assembling a programme like this is flexible, quick and easy, and that's the way radio stations all over the world have been doing it ever since Cool Edit (Audition's predecessor) came into existence somewhat over twenty years ago.

Those gaps between the files you've recorded are your gaps - but you can shrink and expand them to your heart's content. You can even overlap and crossfade them if you want - the world's your oyster.