Feature dataset names containing apostrophes can not be deleted or renamed in ArcCatalog or with ArcObjects.
Apostrophes are not handled correctly with feature dataset names. The apostrophe should be contained in single quotes. For example:
"Select NAME from MYTABLE where NAME = 'test''s'
This is a problem in ArcSDE and Personal Geodatabases.
"select NAME from GDB_FEATUREDATASET where NAME = 'test''s'"
"update sde.sde.GDB_FEATUREDATASET set NAME = 'test_s' where NAME = 'test''s'"
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