You can prune back that one limb to make the tree more balanced.
Yes I did after looking at it for a while. I think it looks pretty good now.
I even went out and looked over an old apple tree that I have and whacked off a little of it too!
Daemon,
If your peach tree dies it won’t be because you pruned it too heavily. I wouldn’t think twice about pruning a peach tree like that this time of year. I will note the leaves are a bit light in color. If you have received the kind of rain we’ve received here, your peach tree could be water stressed. In my area, I’m seeing peach trees around here very stressed from too much water.
Now you can mulch a 5’ circle around the base of the tree so it doesn’t have to compete with grass and will more quickly becomes the tree you want it to be. Mulch even helps trees deal with too much water, IMO, because the roots can function right up to the surface of the soil.