There are three ways I'd consider doing this.
Hacky and error-fuelled, "MOVE ALL THE THINGS"
mv ~/MYDIR/* ~/MYDIR/DESTINATIONDIR
This will try to move the destination into itself and will explode:
mv: cannot move ‘~/MYDIR/DESTINATIONDIR’ to a subdirectory of itself, ‘~/MYDIR/DESTINATIONDIR/DESTINATIONDIR’
But it will move [almost] everything else. So it works but it's a bit of a mess. If you need to match hidden files, run shopt -s dotglob beforehand and it'll work.
Moving a list of files manually
Given the short list of things, we can quite easily just list them out with a little bash expansion:
mv ~/MYDIR/{DIR{1,2},file{1,2}} ~/MYDIR/DESTINATIONDIR
If you need hidden files with this method, just include them in the list.
If this list is coming from something else (eg find) it can be tough to ensure the destination is the last argument. You can move the destination to the front with the -t argument. This is a horrible example but highlights when you need it:
find ~/MYDIR/ -maxdepth 1 ! -name DESTINATIONDIR -exec mv -t ~/MYDIR/DESTINATIONDIR {} +
Inverse globbing with shopt, elegance defined.
So let's strike the balance between manually listing and wildcards. By turning on the extended globbing features in Bash, we can select [almost] everything but the destination directory.
shopt -s extglob
mv ~/MYDIR/!(DESTINATIONDIR) ~/MYDIR/DESTINATIONDIR
If you need to match hidden files, run shopt -s dotglob beforehand and it'll work.