i'm taking a Motion template ("Float", to be exact) and trying to alter the timing of some of the movements in it. i grab "Group 2", scoot it 30 frames to the left, the group moves on the timeline...but as i scrub through the timeline, it still starts at the original place! ironically enough, when i go to the end of the clip on the timeline, it clips out early...so it looks like when i scooted the whole group, it somehow trimmed the out point, though keeping the whole group the same length? i dunno, it probably sounds even more confusing to read this, but if any of you have run into this, let i know.
check to make sure that you don't have some effects with keyframes attached to the "group 2" that you moved. If you do, you need to move those effects as well, and they don't always stick with the group, they sometimes go with the project and stay right where they are - don't ask me why, i run into this rarely but it has happened to me.
You might also try duplicating the group and putting it on another layer, then moving it while you've got the inspector panel open so you can see if the in and out points change for you.