Grouped icons fall apart when moving.

So this is a 2-year-old issue and it has not been addressed by Articulate. SMH... Anyway, this may help someone: One of the issues here is that sub-grouped objects can confuse Storyline. Being that it appears to be built, more or less, on a PowerPoint framework, on-screen vector graphic manipulation is quite limited in many key respects. 

If you have objects grouped WITHIN your main group, this could exacerbate the issue outlined at the start of this thread. SL doesn't seem to understand how to manage the multiple grouping relationships, and you try moving the group or resizing it, and it goes pretty haywire. Try ungrouping everything and regroup as one group. It seems to have mostly solved the issue for me.