As the others have said there are many ways to move things around in avid.
One I use a lot is to mark the section required, and select the tracks you want to move on the left hand track selectors, ( they will be in the highlight colour, which used to be pink, now its a blue not that different to the timeline, I change this in the interface setting to something I can easily see)
then alt-copy, or alt-lift, this will put your “sub-sequence” into the source window, beware if you now select a new source clip you can loose it.
Drag the sub-sequence to a bin if you may need it again.
You can then insert or overwrite into the timeline where and onto which tracks you want.
Steve