Thank you for writing.
You could do with with several small trees including the ornamental trees and some fruit trees.  I could do a better job with a picture of your back yard and a picture of that row of arborvitae.
Too the ones on this list, I would add Junipers, and fruits.  Do not go with magnolias--they are too susceptible to scale. 
https://www.kare11.com/article/life/home-garden/grow-with-kare/grow-with-kare-trees-for-small-spaces/89-bcc7ce52-6f83-480b-ad93-b1f2aa28c7fd

Steve, Thank you so much for your reply! Below are some pictures of our back yard. The five junipers we have are in even worse condition than they look in the picture. Not sure if they didn't get enough sun or water but they always seemed to have some dead spots in them.  I do like having the green trees to look out at. We would be looking to put the shade tree (I know it will take many years before it becomes a shade tree) in the spot where the ash tree is currently.  A crap tree was suggested to us but that seems so messy and we have a dog. Any suggestions are appreciated. Thank you again!

Thank you for the pictures.
You have a lot of problems with this space.

The pavers appear to be non-permeable, if so they will divert water off of the backyard adding to dehydration. This may be even worse because of the pavers retaining heat--adding to stress on plants.  Consider (high budget) permeable pavers to make more effective use of rainfall.

The arbovitae (junipers?) are too close to the fence. This means that half of the plant does not get sun and also, it impairs air circulation around the plant--adding to stress on the plant. There is little to do for this except pulling up some pavers in the middle picture to create a broader planting rim next to the fence.  

The top picture shows a wider planting area but again the plants are too close to the fence. It might be better to remove those plants and put in a new line of plants equally far from the fence and the pavers.

Coming diagonally out of the corner from the ash, you could plant a small tree. If you do not want fruit fallin, a strawberry shortcake hydrangea or a dwarf gingko would be interesting. Both grow fast to a modest height.

Thank you for the helpful feedback. Bachman’s did the landscaping for us and I agree that they planted the trees to close to the fence and they were never able to thrive there. 

Thank you for writing back. 
This is a lovely small tree. https://firsteditionsplants.com/product/vanilla-strawberry-hydrangea/
I like variegated willows. https://www.monrovia.com/dappled-willow.html

Crabapples have a brief show and are then done. 

Thank you for writing back. 
The Apollo sugar maple gets 30 feet high and is 12 feet wide. Thus if you add 2 feet around the tree, it would be 14 feed wide and would have to be 7 feet from the fence.  On the north side of the tree--the shadow would extend 45 feet from the trunk. Can you do this?  

Very helpful! I’ll do some measurements. Thank you!
Tricia 



I am sorry to have made a mistake, 
On the north side of the tree--the shadow would extend 45 feet from the trunk. 
This should say 15 feet from the trunk at noon in Mid June. At the sun got lower in the sky, the north shadow would get longer.  During the day the east and west shadows would be about 22 feet from the trunk because the sun is lower in the sky in the morning and afternoon.  The late summer north shadow would be longer as the sun moves lower in the sky.  

Thank you for the update!

Tricia,
I am embarrassed. Measure your lawn and make a drawing. Indicate North.