I've repaired damage like that. Here's a tip I did;
I peeled the metal back from the corner and then removed the wood from the corner top to bottom. Then I took a 4x4 Heart Redwood beam. I cut a 2x2 section out of one corner, making an "L" shaped corner board. This is better than trying to use two separate 2x4's or other lumber as it's one piece. I used redwood because of it's rot resistance when moist. You can use Doug Fir, pine, heck even oak if you wish! I then installed T nut inserts that take bolts instead of wood thread screws.
I then reattached the siding and mounted the jacks using screws into the T nuts instead of the wood screws that had been holding the jack bracket.
