I can't tell from the picture...do the peeling branches have foliage on them? If not, they're dead and can be pruned away. The center could use cleaning out removing all those small, crossing branches. Looks like a very old plant.

Sumacs can be short-lived. Yours is big and old...... If it's on the way out, it may begin suckering near the base.

Callirhoe: most of the peeling branches are dead, but a couple of them do have leaves at the tips.

It's definitely old; like I said in the post, I've lived here nearly five years and it's always been this size.

It's probably at the end of its life. You can trim off the dead and leave it, or cut it down and see if new suckers emerge. Or you can start with a fresh plant.