The bark damage is concerning and likely causing the stunting on that side of the tree. The sapwood which supplies stems and leaves with water and nutrients is just underneath the bark; if exposed or wounded, it can become infected or killed. You can keep the tree for now and prune away any dead branches (or those that may die back in the next month or so), though it's possible the long-term performance of this tree is in question. We cannot determine exactly what caused the trunk damage; frost cracks, sunscald, and mechanical injury (even prior to purchase) are all possible. No treatments are appropriate except to give the tree time to recover, if it is able.

Check the planting depth; trees should sit with their root flares just at/under the soil surface. It is not uncommon for nursery-grown trees to sit too deeply in their pots with the root flare buried too far. You can gently excavate around the base of the trunks of all of the trees to see where the root flare is situated; this is the location where main roots begin to branch off of the trunk. Although re-planting the trees to correct depth issues may be impractical, you might be able to expose them sufficiently as-is. Once you find them, you can lightly cover them back up with a sprinkling of soil; mulch over the root zone is beneficial, but keep it away from the base of the trunk so the bark can breathe.

These dogwoods appear to be sited in full sun, a condition that they tolerate but which can be stressful for them in summer. If so, be mindful of supplemental watering that may be needed during dry spells in summer and autumn. Dogwoods are adapted to growing in open woodlands and woods' edges, where they receive a bit of shade during the hotter hours of the day. They have minimal tolerance for constantly soggy soils, so check the soil moisture a few inches beneath the surface prior to watering. (In other words, rather than watering on a schedule, monitor them for their needs, which will change with season and the plant's age.) Reducing stress gives trees the best chance at surviving damage and avoiding pest or disease issues.

Miri

Hi

thank you for your advice. So I did removed a lot of the dirt. Did I remove enough of the soil to expose the root flare?? Can you please tell me if the area (circled in red in the picture) is the root flare?? It looks like that part is wider, and it doesn’t have those bark on it. However, I didn’t see the root starting to branch out, so I’m confused if I need to remove more soil

It looks like that may be the root graft, and the root flare would be beneath that.
You can attempt to expose more but that looks like quite a bit of peeling bark and that doesn't bode well for the long-term survival of the tree. It may limp along for a while but is not likely to recover.


Christine

Thank you. I will expose more soil. Any reason why the bark keep on peeling?? How do I prevent that from happening??

A number of reasons could be behind the bark cracking, and it is difficult to determine which was the initiator after the fact. Environmental conditions are very likely (frost cracks, sunscald, transportation injury that bruised too much sapwood, etc), though infection or wood-boring insect infestation are possible. Either of the latter two issues are promoted by general plant stress as young, healthy, vigorous trees are less vulnerable. The initial trigger for the bark loss is probably long gone and there is nothing that can be done to prevent it from progressing; even an active pest or disease is well beyond treatment once external damage like this is apparent.

The root flare being buried could have encouraged or hidden a girdling root. This happens when a root does not head outwards from the trunk (as it should) but instead coils partially around the trunk base or overlaps other major roots. In effect, it "strangles" the cambium (sapwood tissues moving water, nutrients, and carbohydrates throughout the tree) which causes tissue death above below that point. Because tree wood (trunks, roots, and branches) increases in girth as it matures, the outward push of the girdling root along with the wood beneath it make the problem progressively worse as they press into each other more severely. Sometimes girdling roots can be severed in order to save the rest of the tree, but sometimes the loss of that root also causes some canopy dieback, so taking action can be a trade-off with benefits that aren't guaranteed.
https://extension.umd.edu/hgic/topics/girdling-roots

Miri