Your trees present a puzzle.  Crape myrtle scale, https://content.ces.ncsu.edu/crapemyrtle-bark-scale, is rampant here and can cause tree or branch death. Since the insects must crawl, their movement from tree to tree and limb to limb is slow.  It looks as if the part that is leafless is separate from other branches, so it is conceivable that only 1 part of the tree is infested.  You should be able to see the scale on your tree.  Check the still living part. Unfortunately, treatment is difficult without using a systemic pesticide, which affects all insects, including pollinators, that feed on the tree. 
The other possibility is root damage on one side.  Voles are not known to bother crape myrtle, however moles’ tunnelling can leave air pockets around roots, which can cause those roots to die. Has there been any trenching on that side of the tree?

About your flowering apricot: These trees are very susceptible to frost damage, so the lower branches may have lost leaf buds while newer, higher growth was undamaged.  Scratch the bark of apparently dead branches and look for green just under the surface  this means branches are still alive.  If so, see how it does next year.  If not, prune out dead branches  NCSU, https://plants.ces.ncsu.edu/plants/prunus-mume/ has good info about pests of flowering apricot. 

Good idea.