New member here but I've used sketchup a lot. Yeah, move works ok when you select the right segments but there are often unintended effects.
I agree with WalnutAvenue that using components (Group command) is a great way (heck, the only) to go. You can put components into other components which makes for pretty easy manipulation of sub assemblies.
On the other hand, sometimes it's easier to redraw something than trying to fix it. And sometimes, fixing things makes a worse mess of it all! I've gotten really quick at making small components. The order you do things in really effects how easy it is. So to create a mitered box, I would draw the outline from the top (2 rectangles, one inside the other), draw the miter lines (corner to corner) and then use push/pull to lift each side to the correct height. You can control the height by typing in the number in. Push/Pull works best if you rotate the view to an angle. The miters come along for the ride. SU has lots of little helping aspects, like in the push/pull, you do the first one and then if you do an adjacent one, it will stop at that height for a perfect match.
One other trick I use a lot is the intersection command. This works great for lots of stuff. An example - mortise and tenons. You build the tenon component and put it where you want it to be. Select the tenon and the component where you want the mortise and then use intersect/selected. Then go into the mortise component and delete the surfaces you don't want.
And, I use hide/unhide a LOT. makes it easier to see what's going on.