In view to enjoy more sun, I always move some containers from one place to the other such as from back yard in the morning then move to front yard in the afternoon. Would that be not good for the fig tree to grow ?

Hi pacifica,
While moving them, you shake them. They don't like to be shaken - mine at least - that makes them loose the figs.
When positioning them, avoid changing the orientation of the tree. The leaves need to look at the sun, and they do when they grow in one place like they normally do.
If you rotate the tree, then leaves will potentially face the shade ... and won't be efficient at photosynthesis.

After making some room in my compost pile (reduce height and footprint), I installed two pots next to the compost pile - I will no longer move them until the end of the season. I don't want to fool the trees and perhaps shock them nor disturb them .
I know their roots will escape the pots and grow into the soil of the compost pile - that is my goal .

Good luck, keep us posted and tell us if it worked well for you !

Thank you so much for telling me not to shake the plants in pot if possible. I really appreciate it very much as I do not know this at all. 
Have a good day !

sounds like its more not good for your back. =)

I guess there's nothing to do in Hawaii but move fig trees back and forth twice a day :)

It's hard for me to imagine how a yard could be shaped and sized so that there's one spot that gets 4 hours of sun in the morning, another spot that gets 4 hours in the afternoon, but nowhere that gets more than 4 hours combined.  Geometrically it seems like you'd have to have a very tall row house that faces east or west, a front and back yard that were each very very small (5 feet or less deep?), and a lot of trees or buildings just on the other side of where each yard ends.

If that's all the sun I had to work with, I'd probably either move or take up a different hobby.  Surfing maybe?

"Full Sun" is not always desirable, depends on where you are located, altitude, coastal breezes, etc.  At 3000' altitude in North Carolina mountains "Full Sun" has different effect than 6' altitude in Okeechobee, Florida or 300' Del Rio Texas.

If I had to move my trees. I would not be playing with figs.

My house is not huge. The back yard is facing to the East, so my fig trees can get full sun from 9:00 am till 2:00 pm, then front yard is facing to the West and will get full sun from 11:30 am till 5:30 pm. To place all potted fig trees in the front yard might create opportunity from stealing especially overnight.
I found the one that I planted in ground in the front yard will get more ripen figs than those I potted or in ground in the back yard. 

Make a fig mobile. A friend has one for her flowers -- greenhouse on big wheels.

Maybe time to relocate.

Honestly probably worth the investment of trimming some trees if they are causing the shade...