You are working with lines which are rendered in their simplest, default, settings. There MUCH more you can do with Lines. OG is great specifically because it is a simple tool, and you control everything (it's default operation is therefore simple).
You have not told OG anything about what you want with the lines, so when you move the parent, it "correctly" moves the lines-with-no-settings with it. Other users may want that behaviour (certainly I do, until I "set" the lines somewhere).
You might need to use Undo twice, to reverse the two (automatic) actions OG did for you.
Let me assure you that I have hundreds of technical architecture diagrams, some very complex, with important meaning in the lines, and I have no problem at all. It may help to learn the product a little more. The tutorials and example docs are quite helpful.
A line is defined by:
• starting point (red dot)
• ending point (green dot)
• any number of true midpoints (blue dot)
The little blue rectangle on the line means it is just the default midline handle (no true midpoints have been set). Such lines will (predictably) move when you move either the parent or the child, they are good to use when the position of the parent and child are stable.
Any point is highlit when it is selected. You can grab it and move it around.
Try this. Using your example org chart, Services parent at top, a group of 14 children at level 4. Double-click on the line to create a true midpoint (Option-click creates a label; those actions can be reversed via Preferences). Lets say you want the horizontal lines (between parent and children) to remain at level 4. Just above each of the children, on each connecting line, double-click to create a Midpoint, a blue circle replaces the default midline, and place that Midpoint where you want the horizontal line to be, related to each child, and close to it.
Now when you move the parent, the lines will remain with the children.
Try it the other way. Lets say we want the lines to move when we move the parent. In your org chart, start with Services sitting at level 3, one level above its level 4 children. Double-click, create your Midpoints for each connecting line, but place them where you want the horizontal lines to be relative to the parent. This means all Midpoints will be close to the single parent.
To select multiple objects, simply hold the Shift-select, or drag, or shift-drag.
Select the parent and all the lines that you want to move with the parent. You can accomplish this with one drag (from a point just outside the top left of Services, drag to a point just outside the bottom right). Services and 14 lines should be highlit. You can also select each line using select and the shift-select.
Now pick up Services and move it to level 1.
All the Midpoints in a line ware selected when you select the line.
To select a single Midpoint, select the line and then select a Midpoint.
It is a simple tool, you use it at simply or as deeply as you want. It does nothing more or less than you have set.
When you are drawing charts where the position of the parent and child keep changing (eg your org chat, before the four levels were laid out), then it is a good thing to use avoid Midpoints (Inspector/Style/Lines&Shape/RemoveMidpoints).
If you want to improve the percision in your drawing, you can use the grid, set it up for your needs, and place all lines and Midpoints precisely on the grid.
After you have mastered the above to your satisfaction, you can play with:
• lines that have multiple midpoints
• placing a bunch of lines in a Group (use the group button or command-shift-g)
• Group lines with a shape
• change the colour, weight and Endings of lines (or a group together)
• use the Inspector/Style/Lines&Shapes