It sounds like you want to terminate....I would say something or write something along the lines of

"It is not an easy decision but I am very concerned that Susie is not settling into our daycare or into our group the way I had hoped so I think it would be best for everyone if we discontinue our daycare arrangement. I have concerns that she will not be happy or thrive in this group and it is causing the other children some unrest when they see her upset. Ideally, I want everyone to have the best possible environment to come to every day and I feel like this is not a good fit. I would suggest an end date of ________."

I don't think the father's comment is that rude or that your comment was that bad. I think he was probably thinking out loud or just concerned about his little girl.
And I can feel your pain - there isn't really a good answer to that. I also think you are right about why she cries. She probably thinks of alphagetti as the mean person who takes her away from her parents every day.

I hope your day gets better from here on in