Let’s start with the wounded tree first. Trees have an amazing capacity to heal themselves.  How long ago did you make the cut that removed the branch collar?  It’s more challenging for a tree cut like that to compartmentalize the wound, but it looks like it’s trying to do so.  I have two concerns—any wound, especially in cold rainy weather like we have in the PNW—creates an ideal environment for the entrance of plant diseases or insects.  The other concern is that it may have weakened the branch where the wound winds down vertically.  Keep an eye on that.  I don’t think you need to do anything to it at this time.

Now for your other tree.  I consulted with a colleague about it who knows more about pruning than I do. It looks like it’s healthy with vigorous growth.  I think you can have a productive peach tree.  I’ve attached a photo of the one branch that definitely should be removed because it’s growing into the center space of the tree branches, and appears to be crossing other branches—both no-no’s with trees.  In fact, it’s always a good idea to remember the 4-D’s when it comes to pruning.  These 4-Ds should be removed any time of the year when you observe them:

·      Damaged

·      Dead

·      Diseased

·      Dysfunctional (competing branches, crossing, rubbing, water sprouts, suckers, and etc.)

I’m assuming that you did your spring pruning just before the blossom opened.  That’s the time to prune out any gray, non-fruiting shoots, and leaving the reddish colored one-year shoots. In addition, summer pruning in the first two weeks of July, can, and perhaps, should be done on peach trees in order to remove some of the vigorous new growth that shades the interior of the tree, but be sure to complete the pruning before mid-July.  Most pruning cuts should be thinning cuts, where you trim off a branch down to its origin on a larger branch.  Heading cuts, for the most part, should be avoided—heading cuts are what you make when you trim a hedge—just lopping off the end of the branch (https://extension.wsu.edu/maritimefruit/pruning-tree-fruit-the-basics/).  Here is a good video from NC Extension  that will walk you through how to prune your peach trees. https://www.youtube.com/watch?v=ShNGGuO1x4E  From WSU: “Peaches and nectarines bear fruit only on one-year wood, that is, the shoots that grew the previous season produce this season’s fruit. Half or more of each season’s new shoots usually need to be thinned out, to prevent crowding and make room for fruit to grow.”  These are the shoots you want to remove by mid-July.  In fact—good summer pruning will make spring pruning much easier.

Here’s another excerpt that also explains the concept:

Time of Pruning

Peach trees can be pruned in the summer or during the dormant season, but the objectives of pruning vary with time of pruning. Summer pruning is performed in July,  to select scaffold branches on young trees and to redirect the growth of young scaffold branches. For fruiting age trees removing upright and vigorous shoots in June and July will reduce shading to maintain fruiting wood in the canopy interior. Light during June and July, but not later in the season, is critical for flower bud development. Summer pruning to reduce shade two to four weeks before harvest will moderately increase fruit red color, but fruit size and sugar levels will be unaffected. Dormant pruning is used to remove upright and vigorous shoots that shade the tree interior, to limit the size of the tree and to remove excess fruiting shoots. Dormant pruning alone will not reduce shading enough to maintain fruiting wood in the lower regions of the canopy. Trees that are summer pruned each year often require little dormant pruning. Pruning temporarily reduces a tree's tolerance to low temperatures. Therefore, avoid pruning before late February and before predicted low temperatures.

https://extension.psu.edu/peach-tree-pruning-managing-light-and-crop-load