In my 15 years of childcare experience, I have only had to terminate (fire) 3 families. Each one of them had a child that I was not qualified to help.(severe ADHD and behavioral issues) I let the parents know how and what the child is doing every day, this is where my daily journal helps as the parents get a copy of what we did each day and how their child related to the program.
If I know that I cannot and will not deal with this situation I let the parent know that their child is not fitting in emotionally or socially and that I believe it would better the child and family to find alternate arrangements. I give them a letter of termination at this time (and keep a copy in their file) letting them know that the contract will be terminated in 1 month. This gives the family plenty of time to find alternate arrangements.
I believe that if I am not happy caring for the children, I cannot offer them a happy quality day of care.
Good luck, I know that this can be a very stressful issue in your daycare.