moving multiple layers/clips not working

Where exactly are you trying to move those clips? You have a clip in the primary storyline and a clip that is connected to it. If, as it seems, you are trying to move them above the primary, it won’t work this way. You could first “Lift from Storyline”, which will connect them both to a gap clip, and then you should be able to move.

It looks like you’re trying to move a clip on the primary storyline with a connected clip attached to it. There is a gap clip in front of It. Where are you trying to move it to? Of you’re trying to move into into the gap clip area, try using the ripple tool to shorten the gap and let the timeline move the clips.