This is another good example of the usage of "pekee" (vs. "peke ya...") - it mostly translates as "only" as an adjective, while "peke ya~" is by oneself. ;)
(Yes, I just wrote here instead of the original discussion where peke vs. pekee started.)
I don't feel "yeye" is necessary here. "Ni mtoto pekee" should be accepted. This would be particularly true in a context such as "Tatu alifiwa na mama yake. Ni mtoto wa pekee" in other words, Tatu was bereaved of her mother [Tatu's mother died]. She is the only child.