difference between
"We don't want everybody to know about it."
and
"We don't want everybody knowing about it."
difference between
"We don't want everybody to know about it."
and
"We don't want everybody knowing about it."
"want" is an infinitive verb and it can only be followed by (noun/pronoun) to + conjugated form of verb (1). This means that your second sentence isn't correct grammatically.