Dear …
I have been working for __(company name)__ for __(# months/years)__ now and quite enjoy my job.  This really is a great company to work for and I am happy to be here.  For __(# months/years)__, I had worked the __(type/name)__ shift, which proved to blend in well with my home life.  Unfortunately, however, I have found that I am really struggling with the new __(type/name)__ shift that I have recently been scheduled on. 
The reason the __(type/name)__ shift worked so well for me was because __(briefly describe it worked so well for you.)__.  It gave me the opportunity to __(list some things that it allowed you to do)__.  With the new __(type/name)__ shift, I have found it has become increasingly more difficult to __(briefly describe what it is inhibiting in your life)__.  
Therefore, I am requesting that you consider changing my hours __(to/back to)__ to the __(type/name)__ shift.  This would remove the hardship I am currently experiencing with trying to maintain these new hours.  I would be so grateful to you if you could find a way to make these changes for me.  My __(children/spouse/disabled mother/etc.)__ would also greatly appreciate anything you could do to help us in this way. 
Thank you for taking the time to consider my request.  I remain hopeful of your decision.  
Respectfully yours,