If you grab a layer in the timeline with the selection tool (v) and drag the layer it will move all the keyframes and the in and out point for that layer. If you just want to move the keyframes then I would expand the timeline so it fills the entire screen by selecting the timeline and pressing the ~key. Then select all of the layers that you want to adjust the timing for and press the u key to reveal all keyframes. With the selection tool drag Marquis around all of the keyframes and then drag them into their new position.
I may be mistaken but I think losing key frames when moving layers is a 2015 bug isn't it? I seem to remember reading that somewhere.