[Lizard]

I *think* I follow what you're trying to do, provide more detail if my suggestions seem irrelevant.

1) As soon as you drag the start date of a task, it automatically changes from "as early as possible" to "on scheduled date". So if a task is "on scheduled date", it will try not to move as a result of other changes, like moving the group it is in.

2) If you want group 2 to start when group 1 ends, the best way to do this is to leave all your tasks "as early as possible" and create a finish->start dependency from group 1 to group 2. Then even if group 1 gets delayed a bit, group 2 will update with it.